Three-dimensional batteries with compressible cathodes

ABSTRACT

A secondary battery for cycling between a charged and a discharged state is provided. The secondary battery has an electrode assembly having a population of anode structures, a population of cathode structures, and an electrically insulating microporous separator material. The electrode assembly also has a set of electrode constraints that at least partially restrains growth of the electrode assembly. Members of the anode structure population have a first cross-sectional area, A 1  when the secondary battery is in the charged state and a second cross-sectional area, A 2 , when the secondary battery is in the discharged state, and members of the cathode structure population have a first cross-sectional area, C 1  when the secondary battery is in the charged state and a second cross-sectional area, C 2 , when the secondary battery is in the discharged state, where A 1  is greater than A 2 , and C 1  is less than C 2 .

CROSS REFERENCE TO RELATED APPLICATIONS

This application is a U.S. National Phase Application of InternationalApplication PCT Appliation Number PCT/US17/61892, filed Nov. 16, 2017,which claims priority to U.S. Application Ser. No. 62/422,983 filed Nov.16, 2016. The disclsoures of which are incorporated herein by reference.

FIELD OF THE INVENTION

This disclosure generally relates to structures for use in energystorage devices, to energy storage devices employing such structures,and to methods for producing such structures and energy devices.

BACKGROUND

Rocking chair or insertion secondary batteries are a type of energystorage device in which carrier ions, such as lithium, sodium,potassium, calcium or magnesium ions, move between a positive electrodeand a negative electrode through an electrolyte. The secondary batterymay comprise a single battery cell, or two or more battery cells thathave been electrically coupled to form the battery, with each batterycell comprising a positive electrode, a negative electrode, amicroporous separator, and an electrolyte.

In rocking chair battery cells, both the positive and negativeelectrodes comprise materials into which a carrier ion inserts andextracts. As a cell is discharged, carrier ions are extracted from thenegative electrode and inserted into the positive electrode. As a cellis charged, the reverse process occurs: the carrier ion is extractedfrom the positive and inserted into the negative electrode.

When the carrier ions move between electrodes, one of the persistentchallenges resides in the fact that the electrodes tend to expand andcontract as the battery is repeatedly charged and discharged. Theexpansion and contraction during cycling tends to be problematic forreliability and cycle life of the battery because when the electrodesexpand, electrical shorts and battery failures occur.

Therefore, there remains a need for improving the reliability and cyclelife of secondary batteries having electrodes that tend to expand andcontract.

SUMMARY

Briefly, therefore, one aspect of this disclosure relates to theimplementation of constraint structures to improve the energy density,reliability, and cycle life of batteries.

According to one aspect, a secondary battery for cycling between acharged and a discharged state is provided, the secondary battery havinga battery enclosure, an electrode assembly, carrier ions, and anon-aqueous liquid electrolyte within the battery enclosure. Theelectrode assembly has a population of anode structures, a population ofcathode structures, and an electrically insulating microporous separatormaterial electrically separating members of the anode and cathodestructure populations, wherein the anode and cathode structurepopulations are arranged in an alternating sequence in a longitudinaldirection, each member of the anode structure population has a firstcross-sectional area, A₁ when the secondary battery is in the chargedstate and a second cross-sectional area, A₂, when the secondary batteryis in the discharged state, each member of the cathode structurepopulation has a first cross-sectional area, C₁ when the secondarybattery is in the charged state and a second cross-sectional area, C₂,when the secondary battery is in the discharged state, and thecross-sectional areas of the members of the anode and cathode structurepopulations are measured in a first longitudinal plane that is parallelto the longitudinal direction. The electrode assembly also has a set ofelectrode constraints that at least partially restrains growth of theelectrode assembly in the longitudinal direction upon cycling of thesecondary battery between the charged and discharged states. Each memberof the population of cathode structures has a layer of a cathode activematerial and each member of the population of anode structures has alayer of an anode active material having a capacity to accept more thanone mole of carrier ion per mole of anode active material when thesecondary battery is charged from a discharged state to a charged state,and A₁ is greater than A₂ for each of the members of a subset of theanode structure population and C₁ is less than C₂ for each of themembers of a subset of the cathode structure population. The chargedstate is at least 75% of the rated capacity of the secondary battery,and the discharged state is less than 25% of the rated capacity of thesecondary battery.

According to yet another aspect, a method of formation is provided for asecondary battery, the secondary battery being capable of cyclingbetween a charged and a discharged state. The secondary battery has abattery enclosure, an electrode assembly, carrier ions, and anon-aqueous liquid electrolyte within the battery enclosure. Theelectrode assembly has a population of anode structures, a population ofcathode structures, and an electrically insulating microporous separatormaterial electrically separating members of the anode and cathodestructure populations. Members of the anode and cathode structurepopulations are arranged in an alternating sequence in a longitudinaldirection, and members of the population of anode structures have anodeactive material layers that expand in cross-sectional area A uponcharging of the secondary battery. Members of the population of cathodestructures have compressible cathode active material layers having across-sectional area C, the cross-sectional areas being measured in afirst longitudinal plane that is parallel to the longitudinal direction.The method includes, in an initial formation stage, charging thesecondary battery such that an expansion in cross-sectional area of theanode active material layers in the members of the population of anodestructures compresses the compressible cathode active material layers ofthe population of cathode structure, such that a cross-sectional area ofmembers of a subset of the cathode structure population decreases froman initial cross-sectional area C₁ prior to the initial formation stageto a post-formation cross-sectional area C_(f) after the initialformation stage that is less than 95% of the initial cross-sectionalarea C₁ prior to the initial formation stage.

According to yet another aspect, a method of formation is provided for asecondary battery, the secondary battery being capable of cyclingbetween a charged and a discharged state. The secondary battery has abattery enclosure, an electrode assembly, carrier ions, and anon-aqueous liquid electrolyte within the battery enclosure. Theelectrode assembly has a population of anode structures, a population ofcathode structures, and electrically insulating microporous separatorselectrically separating members of the anode and compressible cathodestructure populations. Members of the anode and cathode structurepopulations are arranged in an alternating sequence in a longitudinaldirection, and members of the population of anode structures have anodeactive material layers that expand in cross-sectional area A uponcharging of the secondary battery. Members of the population of cathodestructures have compressible cathode active material layers having across-sectional area C, the cross-sectional areas being measured in afirst longitudinal plane that is parallel to the longitudinal direction.The method includes, in an initial formation stage, charging thesecondary battery such that expansion of the anode active materiallayers in the members of the population of anode structures compressesthe microporous separators against the compressible cathode activematerial layers of the cathode structures at a pressure that contractsthe cross-sectional area C of the compressible cathode active materiallayers, while also at least partially adhering the microporousseparators to the compressible cathode active material layers of thecathode structures and the anode active material layers of the anodestructures, wherein, upon discharge of the secondary battery andcontraction in the cross-sectional area A of the anode active materiallayers, the at least partial adhesion of the microporous separators tothe compressible cathode active material layers and the anode activematerial layers causes expansion in the cross-sectional area C of thecompressible cathode active material layers.

According to yet another aspect, a secondary battery for cycling betweena charged and a discharged state is provided, the secondary batteryhaving a battery enclosure, an electrode assembly, carrier ions, and anon-aqueous liquid electrolyte within the battery enclosure. Theelectrode assembly has a population of anode structures, a population ofcathode structures, and an electrically insulating microporous separatormaterial electrically separating members of the anode and cathodestructure populations. The electrode assembly also has a set ofelectrode constraints that at least partially restrains growth of theelectrode assembly in the longitudinal direction upon cycling of thesecondary battery. Members of the population of anode structures have ananode active material, and wherein the anode active material has thecapacity to accept more than one mole of carrier ion per mole of anodeactive material when the secondary battery is charged from a dischargedstate to a charged state. Members of the population of cathodestructures have a porous cathode active material, wherein a volume V₂ ofthe porous cathode active material occupied by the non-aqueous liquidelectrolyte in the discharged state is greater than a volume V₁ of theporous cathode active material occupied by the non-aqueous electrolytein the charged state. The charged state is at least 75% of the ratedcapacity of the secondary battery, and the discharged state is less than25% of the rated capacity of the secondary battery.

According to yet another aspect, a secondary battery for cycling betweena charged and a discharged state is provided, the secondary batteryhaving a battery enclosure, an electrode assembly, carrier ions, and anon-aqueous liquid electrolyte within the battery enclosure. Theelectrode assembly has a population of anode structures, a population ofcathode structures, and an electrically insulating microporous separatormaterial electrically separating members of the anode and cathodestructure populations. Members of the population of anode structureshave an anode active material, and members of the population of cathodestructures have a cathode active material. Members of the population ofcathode structures have an areal capacity of at least 5 mA·h/cm² at 0.1C, and a rate capability of 1 C:C/10 of at least 80% for discharge froma charged state to a discharged state. The charged state is at least 75%of the rated capacity of the secondary battery, and the discharged stateis less than 25% of the rated capacity of the secondary battery.

According to yet another aspect, a secondary battery for cycling betweena charged and a discharged state is provided, the secondary batteryhaving a battery enclosure, an electrode assembly, carrier ions, andanon-aqueous liquid electrolyte within the battery enclosure. Theelectrode assembly has a population of anode structures, a population ofcathode structures, and an electrically insulating microporous separatormaterial electrically separating members of the anode and cathodestructure populations, wherein members of the anode and cathodestructure populations are arranged in an alternating sequence in alongitudinal direction. Each member of the population of anodestructures has a layer of an anode active material and each member ofthe population of cathode structures has a layer of a cathode activematerial. Each member of the population of cathode structures has afirst cross-sectional area C₁ when the secondary battery is in thecharged state, and has a second cross-sectional area C₂ when thesecondary battery is in the discharged state, wherein the secondcross-sectional area C₂ of the cathode structures in the dischargedstate is greater than the first cross-sectional area C₁ of the cathodestructures in the charged state, and wherein a ratio of secondcross-sectional area C₂ of a subset of the members of the population ofcathode structures to the first cross-sectional area C₁ of the subset ofthe members of the population of cathode structures is at least 1.05:1upon discharging of the secondary battery from the charged state to thedischarged state. The charged state is at least 75% of the ratedcapacity of the secondary battery, and the discharged state is less than25% of the rated capacity of the secondary battery.

Other aspects, features and embodiments of the present disclosure willbe, in part, discussed and, in part, apparent in the followingdescription and drawing.

BRIEF DESCRIPTION OF THE DRAWING

FIG. 1A is a schematic view of one embodiment of an electrode assemblyhaving a population of cathode structures and a population of anodestructures.

FIG. 1B is a perspective view of one embodiment of an electrode assemblyhaving a population of cathode structures and a population of anodestructures.

FIG. 1C is a perspective view of one embodiment of an electrode assemblyhaving a population of cathode structures and a population of anodestructures, and a first longitudinal plane;

FIG. 1D is a cross-sectional view of an embodiment of an electrodeassembly illustrating cross-sectional areas of a population of cathodestructures and a population of anode structures.

FIG. 1E is a cross-sectional view of an embodiment of an electrodeassembly illustrating an opposing surface area of an anode structure;

FIGS. 2A-2C are cross-sectional views of an embodiment of an electrodeassembly with a population of cathode structures

FIG. 3 is a schematic view of an embodiment of a layer of cathode activematerial.

FIGS. 4A-4B are cross-sectional views of an embodiment of an electrodeassembly with cathode structures having layers of cathode activematerial that are porous.

FIGS. 5A-5H show exemplary embodiments of different shapes and sizes foran electrode assembly.

FIG. 6A illustrates a cross-section of an embodiment of the electrodeassembly taken along the line A-A′ as shown in FIG. 1B, and furtherillustrates elements of primary and secondary growth constraint systems.

FIG. 6B illustrates a cross-section of an embodiment of the electrodeassembly taken along the line B-B′ as shown in FIG. 1B, and furtherillustrates elements of primary and secondary growth constraint systems.

FIG. 6C illustrates a cross-section of an embodiment of the electrodeassembly taken along the line B-B′ as shown in FIG. 1B, and furtherillustrates elements of primary and secondary growth constraint systems.

FIG. 6D illustrates a cross section of an embodiment of the electrodeassembly taken along the line A-A1′ as shown in FIG. 1B.

FIG. 7 illustrates a cross-section of an embodiment of the electrodeassembly taken along the line A-A′ as shown in FIG. 1B, furtherincluding a set of electrode constraints, including one embodiment of aprimary constraint system and one embodiment of a secondary constraintsystem.

FIG. 8 illustrates one embodiment of a top view of a porous growthconstraint over an electrode assembly.

FIG. 9 illustrates an exploded view of an embodiment of an energystorage device or a secondary battery having compressible cathodestructures.

DEFINITIONS

“A,” “an,” and “the” (i.e., singular forms) as used herein refer toplural referents unless the context clearly dictates otherwise. Forexample, in one instance, reference to “an electrode” includes both asingle electrode and a plurality of similar electrodes.

“About” and “approximately” as used herein refers to plus or minus 10%,5%, or 1% of the value stated. For example, in one instance, about 250μm would include 225 μm to 275 μm. By way of further example, in oneinstance, about 1,000 μm would include 900 μm to 1,100 μm. Unlessotherwise indicated, all numbers expressing quantities (e.g.,measurements, and the like) and so forth used in the specification andclaims are to be understood as being modified in all instances by theterm “about,” Accordingly, unless indicated to the contrary, thenumerical parameters set forth in the following specification andattached claims are approximations. Each numerical parameter should atleast be construed in light of the number of reported significant digitsand by applying ordinary rounding techniques.

“Areal capacity” as used herein in the context of a secondary batteryrefers to the capacity of the battery per unit area, where the area isthe geometrical area of a portion of an anode structure (ignoringporosity) facing the cathode structure, summed over all anode structuresin the secondary battery. The areal capacity will also typically bespecified at a certain C-rate, such as 0.1 C. For example, if the ratedcapacity of a battery is 1000 mA·h at a C-rate of 0.1 C, and thegeometrical area of the portion of each anode structure facing eachcathode structure is 250 cm², and there are 5 anode structures (eachhaving two facing sides), then the areal capacity is 1000/(250×5×2)=0.4mA·h/cm².

“C-rate” as used herein refers to a measure of the rate at which asecondary battery is discharged, and is defined as the discharge currentdivided by the theoretical current draw under which the battery woulddeliver its nominal rated capacity in one hour. For example, a Crate of1 C indicates the discharge current that discharges the battery in onehour, a rate of 2 C indicates the discharge current that discharges thebattery in ½ hours, a rate of C/2 indicates the discharge current thatdischarges the battery in 2 hours, etc.

“Charged state” as used herein in the context of the state of asecondary battery refers to a state where the secondary battery ischarged to at least 75% of its rated capacity. For example, the batterymay be charged to at least 80% of its rated capacity, at least 90% ofits rated capacity, and even at least 95% of its rated capacity, such as100% of its rated capacity.

“Discharged state” as used herein in the context of the state of asecondary battery refers to a state where the secondary battery isdischarged to less than 25% of its rated capacity. For example, thebattery may be discharged to less than 20% of its rated capacity, suchas less than 10% of its rated capacity, and even less than 5% of itsrated capacity, such as 0% of its rated capacity.

A “cycle” as used herein in the context of cycling of a secondarybattery between charged and discharged states refers to charging and/ordischarging a battery to move the battery in a cycle from a first statethat is either a charged or discharged state, to a second state that isthe opposite of the first state (i.e., a charged state if the firststate was discharged, or a discharged state if the first state wascharged), and then moving the battery back to the first state tocomplete the cycle. For example, a single cycle of the secondary batterybetween charged and discharged states can include, as in a charge cycle,charging the battery from a discharged state to a charged state, andthen discharging back to the discharged state, to complete the cycle.The single cycle can also include, as in a discharge cycle, dischargingthe battery from the charged state to the discharged state, and thencharging back to a charged state, to complete the cycle.

“Feret diameter” as referred to herein with respect to the electrodeassembly is defined as the distance between two parallel planesrestricting the electrode assembly measured in a direction perpendicularto the two planes. For example, a Feret diameter of the electrodeassembly in the longitudinal direction is the distance as measured inthe longitudinal direction between two parallel planes restricting theelectrode assembly that are perpendicular to the longitudinal direction.As another example, a Feret diameter of the electrode assembly in thetransverse direction is the distance as measured in the transversedirection between two parallel planes restricting the electrode assemblythat are perpendicular to the transverse direction. As yet anotherexample, a Feret diameter of the electrode assembly in the verticaldirection is the distance as measured in the vertical direction betweentwo parallel planes restricting the electrode assembly that areperpendicular to the vertical direction.

“Inversely related” as used herein with respect to a change in at leastone dimension (e.g., the width), cross-sectional area, and/or volume ofan electrode structure (e.g., anode structure and/or cathode structure),refers to a sign of the change being the opposite of that of a sign ofthe change in the same dimension, cross-section and/or volume in acounter-electrode structure. For example, for an increase in width of ananode structure, a change in the width dimension of the cathodestructure that is inversely related thereto would be a decrease in widthof the cathode structure. As another example, for an increase in across-sectional area of an anode structure, a change in thecross-sectional area of the cathode structure that is inversely relatedthereto would be a decrease in cross-sectional area of the cathodestructure. Similarly, for a decrease in width of an anode structure, achange in the width dimension of the cathode structure that is inverselyrelated thereto would be an increase in width of the cathode structure.As another example, for a decrease in a cross-sectional area of an anodestructure, a change in the cross-sectional area of the cathode structurethat is inversely related thereto would be an increase incross-sectional area of the cathode structure. By way of furtherexample, for an increase in width of a cathode structure, a change inthe width dimension of the anode structure that is inversely relatedthereto would be a decrease in width of the anode structure. As anotherexample, for an increase in a cross-sectional area of a cathodestructure, a change in the cross-sectional area of the anode structurethat is inversely related thereto would be a decrease in cross-sectionalarea of the anode structure. Similarly, for a decrease in width of acathode structure, a change in the width dimension of the anodestructure that is inversely related thereto would be an increase inwidth of the anode structure. As another example, for a decrease in across-sectional area of a cathode structure, a change in thecross-sectional area of the anode structure that is inversely relatedthereto would be an increase in cross-sectional area of the anodestructure.

“Longitudinal axis,” “transverse axis,” and “vertical axis,” as usedherein refer to mutually perpendicular axes (i.e., each are orthogonalto one another). For example, the “longitudinal axis,” “transverseaxis,” and the “vertical axis” as used herein are akin to a Cartesiancoordinate system used to define three-dimensional aspects ororientations. As such, the descriptions of elements of the inventivesubject matter herein are not limited to the particular axis or axesused to describe three-dimensional orientations of the elements.Alternatively stated, the axes may be interchangeable when referring tothree-dimensional aspects of the inventive subject matter.

“Longitudinal direction,” “transverse direction,” and “verticaldirection,” as used herein, refer to mutually perpendicular directions(i.e., each are orthogonal to one another). For example, the“longitudinal direction,” “transverse direction,” and the “verticaldirection” as used herein may be generally parallel to the longitudinalaxis, transverse axis and vertical axis, respectively, of a Cartesiancoordinate system used to define three-dimensional aspects ororientations.

“Repeated cycling” as used herein in the context of cycling betweencharged and discharged states of the secondary battery refers to cyclingmore than once from a discharged state to a charged state, or from acharged state to a discharged state. For example, repeated cyclingbetween charged and discharged states can including cycling at least 2times from a discharged to a charged state, such as in charging from adischarged state to a charged state, discharging back to a dischargedstate, charging again to a charged state and finally discharging back tothe discharged state. As yet another example, repeated cycling betweencharged and discharged states at least 2 times can include dischargingfrom a charged state to a discharged state, charging back up to acharged state, discharging again to a discharged state and finallycharging back up to the charged state By way of further example,repeated cycling between charged and discharged states can includecycling at least 5 times, and even cycling at least 10 times from adischarged to a charged state. By way of further example, the repeatedcycling between charged and discharged states can include cycling atleast 25, 50, 100, 300, 500 and even 1000 times from a discharged to acharged state.

“Rate capability” as used herein in the context of a secondary batteryrefers to the ratio of the capacity of the secondary battery at a firstC-rate to the capacity of the secondary battery at a second C-rate,expressed as a percentage. For example, the rate capability maycalculated according to Capacity₁/Capacity₂×100, where Capacity₁ is thecapacity for discharge at the first C-rate, such as a C-rate of 1 C, andCapactiy₂ is the capacity for discharge at a second C-rate, such as aC-rate of C/10, and may be expressed as the calculated percentage for aspecified ratio C_(x):C_(y), where C_(x) is the first C-rate, and C_(y)is the second C-rate.

“Rated capacity” as used herein in the context of a secondary batteryrefers to the capacity of the secondary battery to deliver a specifiedcurrent over a period of time, as measured under standard temperatureconditions (25° C.). For example, the rated capacity may be measured inunits of Amp hour, either by determining a current output for aspecified time, or by determining for a specified current, the time thecurrent can be output, and taking the product of the current and time.For example, for a battery rated 20 Amp·hr, if the current is specifiedat 2 amperes for the rating, then the battery can be understood to beone that will provide that current output for 10 hours, and converselyif the time is specified at 10 hours for the rating, then the batterycan be understood to be one that will output 2 amperes during the 10hours. In particular, the rated capacity for a secondary battery may begiven as the rated capacity at a specified discharge current, such asthe C-rate, where the C-rate is a measure of the rate at which thebattery is discharged relative to its capacity. For example, a C-rate of1 C indicates the discharge current that discharges the battery in onehour, 2 C indicates the discharge current that discharges the battery in½ hours, C/2 indicates the discharge current that discharges the batteryin 2 hours, etc. Thus, for example, a battery rated at 20 Amp·hr at aC-rate of 1 C would give a discharge current of 20 Amp for 1 hour,whereas a battery rated at 20 Amp·hr at a C-rate of 2 C would give adischarge current of 40 Amps for ½ hour, and a battery rated at 20Amp·hr at a C-rate of C/2 would give a discharge current of 10 Amps over2 hours.

“Maximum width” (W_(EA)) as used herein in the context of a dimension ofan electrode assembly corresponds to the greatest width of the electrodeassembly as measured from opposing points of longitudinal end surfacesof the electrode assembly in the longitudinal direction.

“Maximum length” (L_(EA)) as used herein in the context of a dimensionof an electrode assembly corresponds to the greatest length of theelectrode assembly as measured from opposing points of a lateral surfaceof the electrode assembly in the transverse direction.

“Maximum height” (H_(EA)) as used herein in the context of a dimensionof an electrode assembly corresponds to the greatest height of theelectrode assembly as measured from opposing points of the lateralsurface of the electrode assembly in the transverse direction.

“Porosity” or “void fraction” as used herein refers to the fraction ofvoids in a volume over the total volume, and may be expressed as apercentage. For example, the porosity of a cathode active material layeris the fraction of volume made up by voids in the layer per total layervolume. In the context of a secondary battery, the voids in a cathodeactive material layer may be at least partially filled with electrolyte,such as liquid electrolyte, during charging and/or discharging of thesecondary battery, and as such the porosity or void fraction may be ameasure of the volume fraction of the layer that can potentially beoccupied by the electrolyte.

DETAILED DESCRIPTION

In general, aspects of the present disclosure are directed to an energystorage device 100 (see, e.g., FIG. 9), such as a secondary battery 102,as shown for example in FIGS. 1A-1B and/or FIG. 9, that cycles between acharged and a discharged state. The secondary battery 102 includes abattery enclosure 104, an electrode assembly 106, carrier ions, and anon-aqueous liquid electrolyte within the battery enclosure. In theembodiment as shown in FIG. 1A, the electrode assembly 106 comprises apopulation of anode structures 110 (i.e., negative electrodestructures), a population of cathode structures 112 (i.e., positiveelectrode structures), and electrically insulating microporousseparators 130 arranged to electrically separate the members of thepopulations of anode structures 110 and 112.

According to one embodiment, aspects of the disclosure are directed toaddressing issues that can arise in energy storage devices 100, such assecondary batteries 102, in a case where members of the population ofanode structures 110 expand and/or contract upon cycling of thesecondary battery 102 between charged and discharged states. Forexample, the anode structures 110 may comprise a layer of anode activematerial 132 (see, e.g., FIG. 7) that accepts carrier ions duringcharging of the secondary battery 102, such as by intercalating with oralloying with the carrier ions, in an amount that is sufficient togenerate an increase in the volume of the anode structure. Referring toFIG. 1A, an embodiment of a three-dimensional electrode assembly 106 isshown with an alternating set of the anode structures 110 and cathodestructures 112 that are interdigitated with one another, and which has alongitudinal axis A_(EA) that is generally parallel to a stackingdirection D (which is depicted as being parallel to the Y axis, in FIG.1A) a transverse axis (not shown) generally parallel to the X axis, anda vertical axis (not shown) generally parallel to the Z axis. The X, Yand Z axes shown herein are arbitrary axes intended only to show a basisset where the axes are mutually perpendicular to one another in areference space, and are not intended in any way to limit the structuresherein to a specific orientation. Generally, upon charge and dischargecycling of a secondary battery 102 having the electrode assembly 106,the carrier ions travel between the anode and cathode structures 110 and112, respectively, such as generally in a direction that is parallel tothe Y axis as shown in the embodiment depicted in FIG. 1A, and canintercalate and/or move into anode/cathode active material of one ormore of the anode structures 110 and cathode structures 112 that arelocated within the direction of travel. In particular, in moving from adischarged state to a charged state, carrier ions such as, for example,one or more of lithium, sodium, potassium, calcium and magnesium, canmove between the positive and negative electrodes in the battery. Uponreaching the anode structure, the carrier ions may then intercalate oralloy into the electrode material, thus increasing the size and volumeof that electrode. Conversely, reversing from the charged state to thedischarged state can cause the ions to de-intercalate or de-alloy, thuscontracting the anode structure. This alloying and/or intercalation andde-alloying and/or de-intercalation can cause significant volume changein the anode structure, which can cause strain in the electrode assembly106, due to an overall macroscopic expansion of the electrode assembly106 that can occur as a result of expansion of members of the populationof anode structures 110 during cycling of the secondary battery 102.Thus, the repeated expansion and contraction of the anode structures 110upon charging and discharging can create strain in the electrodeassembly 106.

According to one embodiment, the anode structures 110 that expand and/orcontract with cycling of the secondary battery comprise an anode activematerial that has the capacity to accept more than one mole of carrierion per mole of anode active material, when the secondary battery 102 ischarged from a discharged to a charged state. By way of further example,the anode active material may comprise a material that has the capacityto accept 1.5 or more moles of carrier ion per mole of anode activematerial, such as 2.0 or more moles of carrier ion per mole of anodeactive material, and even 2.5 or more moles of carrier ion per mole ofanode active material, such as 3.5 moles or more of carrier ion per moleof anode active material. The carrier ion accepted by the anode activematerial may be at least one of lithium, potassium, sodium, calcium, andmagnesium. Examples of anode active materials that expand to providesuch a volume change include one or more of silicon, aluminum, tin,zinc, silver, antimony, bismuth, gold, platinum, germanium, palladium,and alloys thereof.

According to one embodiment, the secondary battery 102 includes a set ofelectrode constraints 108 that restrain growth of the electrode assembly106. The growth of the electrode assembly 106 that is being constrainedmay be a macroscopic increase in one or more dimensions of the electrodeassembly 106, and which may be due to an increase in the volume ofmembers of the population of anode structures 110. In one embodiment,the set of electrode constraints 108 comprise a primary growthconstraint system 151 to mitigate and/or reduce at least one of growth,expansion, and/or swelling of the electrode assembly 106 in thelongitudinal direction (i.e., in a direction that parallels the Y axis),as shown for example in FIG. 1B. For example, the primary growthconstraint system 151 can include structures configured to constraingrowth by opposing expansion, such as at longitudinal end surfaces 116,118 of the electrode assembly 106. In one embodiment, the primary growthconstraint system 151 comprises first and second primary growthconstraints 154, 156, that are separated from each other in thelongitudinal direction, and that operate in conjunction with at leastone primary connecting member 162 that connects the first and secondprimary growth constraints 154, 156 together to restrain growth in thelongitudinal direction of the electrode assembly 106. For example, thefirst and second primary growth constraints 154, 156 may at leastpartially cover first and second longitudinal end surfaces 116, 118 ofthe electrode assembly 106, and may operate in conjunction with one ormore connecting members 162, 164 connecting the primary growthconstraints 154, 156 to one another to oppose and restrain any growth inthe electrode assembly 106 that occurs during repeated cycles ofcharging and/or discharging. In another embodiment, one or more of thefirst and second primary growth constraints 154, 156 may be internal tothe electrode assembly 106, and may operate in conjunction with at leastone connecting member 162 to constrain growth in the longitudinaldirection. Further discussion of embodiments and operation of theprimary growth constraint system 151 is provided in more detail below.

In addition, repeated cycling through charge and discharge processes ina secondary battery 102 can induce growth and strain not only in alongitudinal direction of the electrode assembly 106 (e.g., Y-axis inFIGS. 1A-1B), but can also induce growth and strain in directionsorthogonal to the longitudinal direction, such as the transverse andvertical directions (e.g., X and Z axes, respectively, in FIGS. 1A-1B).Furthermore, in certain embodiments, the incorporation of a primarygrowth constraint system 151 to inhibit growth in one direction can evenexacerbate growth and/or swelling in one or more other directions. Forexample, in a case where the primary growth constraint system 151 isprovided to restrain growth of the electrode assembly 106 in thelongitudinal direction, the intercalation of carrier ions during cyclesof charging and discharging and the resulting swelling of electrodestructures can induce strain in one or more other directions. Inparticular, in one embodiment, the strain generated by the combinationof electrode growth/swelling and longitudinal growth constraints canresult in buckling or other failure(s) of the electrode assembly 106 inthe vertical direction (e.g., the Z axis as shown in FIGS. 1A-1B), oreven in the transverse direction (e.g., the X axis as shown in FIGS.1A-1B).

Accordingly, in one embodiment of the present disclosure, the secondarybattery 102 includes not only a primary growth constraint system 151,but also at least one secondary growth constraint system 152 that mayoperate in conjunction with the primary growth constraint system 151 torestrain growth of the electrode assembly 106 along one or more axes ofthe electrode assembly 106. For example, in one embodiment, thesecondary growth constraint system 152 may be configured to interlockwith, or otherwise synergistically operate with, the primary growthconstraint system 151, such that overall growth of the electrodeassembly 106 can be restrained to impart improved performance andreduced incidence of failure of the secondary battery having theelectrode assembly 106 and primary and secondary growth constraintsystems 151 and 152, respectively. In one embodiment, the secondarygrowth constraint system 152 comprises first and second secondary growthconstraints 158, 160 separated in a second direction and connected by atleast one secondary connecting member 166, wherein the secondaryconstraint system at least partially restrains growth of the electrodeassembly in the direction orthogonal to the longitudinal direction(e.g., the Z direction), upon cycling of the secondary battery. Furtherdiscussion of embodiments of the interrelationship between the primaryand secondary growth constraint systems 151 and 152, respectively, andtheir operation to restrain growth of the electrode assembly 106, isprovided in more detail below.

In one embodiment of the disclosure, the set of electrode constraints108 may constrain the growth of the electrode assembly 106, such thatthe growth of members of the population of anode structures 110, i.e.during charging of the secondary battery 102 having the electrodeassembly 106, results in compression of other structures of theelectrode assembly 106. For example, the set of electrode constraints108 may provide a longitudinal constraint, i.e. via the primary growthconstraint system 151, that constrains growth of the electrode assembly106 in the longitudinal direction, such that expansion of members of thepopulation of anode structures 110 in the longitudinal direction duringcharging of the secondary battery 102 exerts a compressive pressure onmembers of the population of cathode structures 112 in the electrodeassembly 106. That is the members of the population of cathodestructures 112 may be at least partially prevented from longitudinallytranslating away from the expanding anode structures members by thepresence of the longitudinal constraints, with the result thatlongitudinal expansion of members of the population of anode structures110 compresses the members of the population of cathode structures 112.According to yet another embodiment, the set of electrode constraints108 may constrain growth of the electrode assembly 106 in otherdirection(s) orthogonal to the longitudinal direction, such as in thevertical direction (Z direction), and/or in the transverse direction (Xdirection), such that growth of members of the population of anodestructures 110 during charging generates a compressive force. The growthof the members of the population of anode structures 110 in an electrodeassembly 106 having the set of electrode constraints may thus generatecompressive forces and/or pressures on other components of the electrodeassembly, which can lead to failure of such components if a force and/orpressure failure limit is exceeded.

In one embodiment, the expansion and/or contraction of the members ofthe population of anode structures 110 in the constrained electrodeassembly 106 can be at least partially accommodated by providing membersof the population of cathode structures 112 that are capable ofexpanding and/or contracting, such as at least partly in relation to theexpansion and/or contraction of the members of the population of anodestructures 110, thereby reducing strain in the electrode assembly 106.For example, in one embodiment, the members of the population of cathodestructures 112 are capable of changing (e.g., expanding and/orcontracting) in at least one dimension in a manner that is inverselyrelated to a change in at least one dimension of the members of thepopulation of anode structures. For example, in a case where members ofthe population of anode structures 110 increase in a width dimensionand/or cross-sectional area during charging of the secondary battery102, the members of the population of cathode structures 112 may becapable of contracting in the width dimension and/or cross-sectionalarea, to at least partially accommodate the change in dimension(s) ofmembers of the population of anode structures 110.

In one embodiment, each member of a population of anode structures 110has a cross-section 114 with cross-sectional area A, and each member ofthe population of cathode structures 112 has a cross-section 114 withcross-sectional area C, wherein the cross-sectional areas are measuredin a first longitudinal plane 113 that is parallel to the longitudinaldirection (i.e., parallel to the longitudinal axis A_(EA)), as shown forexample in FIGS. 1C and 1D. As seen in the embodiment as shown in FIG.1D, which depicts generally rectangular cross-sections as taken alongthe longitudinal plane 113, the cross-sectional area A of the anodestructure for such a rectangular cross-section may be equal to theheight H_(A) of the anode structure 110 times the width W_(A) of theanode structure, and the cross-sectional area C of the cathode structure112 may be equal to the height H_(C) of the cathode structure 110 timesthe width W_(C) of the cathode structure 112. Alternatively and/oradditionally, the cross-sectional area 114 may be calculated forelectrodes having different shapes and/or cross-sections other than thatshown in FIGS. 1C-1D, for example by a suitable cross-sectional areadetermination method understood by those of ordinary skill in the art.Without being limited thereto, in one embodiment, the cross-sectionalarea may be calculated by using a Scanning Electron Microscopy (SEM)technique to identify a cross-section of a member of the cathode and/oranode structure populations that is of interest, in the firstlongitudinal plane 113. The cross-sectional area for the cross-sectionobtained by SEM may then be obtained using methods known to those ofordinary skill in the art, such as for example by using availablesoftware programs capable of determining the areas of various shapes andobjects, such as for example the ImageJ software (Image Processing andAnalysis in Java) available from the National Institutes of Health. Inone embodiment, the area of a cross-section in an image identified bySEM may be generally determined using a software program bycomputationally or manually identifying the boundaries of thecross-section in the SEM image, counting a number of pixels that fallwithin the identified boundaries of the portion of the SEM imagecorresponding to the cross-section, and inputting a scale of the image(e.g., dimension size per pixel in the image), to calculate the area ofthe identified cross-section. Other methods known to those of ordinaryskill in the art for the determination of cross-sectional areas may alsobe used in determining the area of a cross-section of one or moremembers of the anode and cathode structure populations.

Accordingly, in one embodiment, a change in size of either a member ofthe population of anode structures 110 and/or a member of the populationof cathode structure 112 may be determined according to a change in thecross-sectional area of the structure as measured in the firstlongitudinal plane. For example, in one embodiment, each member of theanode structure population has a first cross-sectional area, A₁, whenthe secondary battery is in the charged state, and a secondcross-sectional area A₂ when the secondary battery is in the dischargedstate, and each member of the cathode structure population has a firstcross-sectional area C₁ when the secondary battery is in the chargedstate, and a second cross-sectional area C₂, when the secondary batteryis in the discharged state. The change in dimension and/or volume of themembers of the population of anode and/or cathode structures uponcharging and discharging may thus result in an assembly where A₁ isgreater than A₂ for each of the members of a subset of the anodestructure population, and C₁ is less than C₂ for each of the members ofa subset of the cathode structure population. That is, upon charging ofthe secondary battery, the cross-sectional areas of members of the anodestructure population increase from A₁ to A₂, whereas the cross-sectionalareas of members of the cathode structure population contract from C₂ toC₁, and upon discharging of the secondary battery, the cross-sectionalareas of members of the anode structure population decrease from A₂ toA1, whereas the cross-sectional areas of members of the cathodestructure population increase from C₂ to C₁. Thus, in one embodiment,the changing dimension(s) of members of the cathode structure populationcan at least partially accommodate an increase and/or decrease in thedimensions and/or size of members of the anode structure population.

Furthermore, by “subset” of the anode structure population, it is meantat least one member of the anode structure population, and the subsetcan also be co-extensive with the number of members in the anodestructure population in the electrode assembly 106. That is, the subsetof the population of anode structures can include only one or allmembers of the population of anode structures in the electrode assembly106, or any number in between. Similarly, by “subset” of the cathodestructure population, it is meant at least one member of the cathodestructure population, and the subset can also be co-extensive with thenumber of members in the cathode structure population in the electrodeassembly 106. That is, the subset of the population of cathodestructures can include only one or all members of the population ofcathode structures in the electrode assembly, or any number in between.For example, the subset of either anode or cathode structure populationscan comprise one member or two members, or more. In one embodiment, thesubset comprises at least five members. In another embodiment, thesubset comprises at least 10 members. In yet another embodiment, thesubset comprises at least 20 members. In yet another embodiment, thesubset comprises at least 50 members. For example, in one embodiment,the subset of the population can comprise from 1 to 7 members, such asfrom 2 to 6 members, and even from 3 to 5 members. In yet anotherembodiment, the subset (of either the anode and/or cathode structurepopulations) can comprise a percentage of the total number of members inthe electrode assembly 106. For example, the subset can comprise atleast 10% of the members (anode and/or cathode members) in the electrodeassembly, such as at least 25% of the members, and even at least 50%,such as at least 75%, and even at least 90% of the memebrs in theelectrode assembly.

By way of further explanation, in one embodiment, the members of thepopulation of cathode structures 112 can be understood to exhibit achange in size, such as a change in dimension, cross-section and/orvolume. For example, members of the population of cathode structure 112may exhibit a change in the cross-sectional areas C, or width W_(C) ofeach cathode structure 112 as measured in the longitudinal direction(i.e., parallel to the longitudinal axis A_(EA)), to at least partiallyaccommodate an expansion/contraction of the anode structures 110. Forexample, in one embodiment, the change in width W_(C) and/orcross-sectional area C of members of the population of cathodestructures 112 may at least partially accommodate a change in widthW_(A) and/or cross-sectional areas A of members of the population ofanode structures 110, such as a width as measured in the longitudinaldirection and/or a cross-section having at least a portion of the widthas a dimension thereof, which may occur due to intercalation and/oralloying or de-intercalation and de-alloying of carrier ions in thedirection of travel of the carrier ions between the anode and cathodestructures, which direction of travel may generally be in thelongitudinal direction. That is, in a case where members of thepopulation of anode structures 110 increase in width and/orcross-sectional area upon charging, the members of the population ofcathode structures 112 may decrease in width and/or cross-sectional areaupon charging, and in a case where members of the population of anodestructures 110 decrease in width and/or cross-sectional area upondischarging, members of the population of the cathode structures 112 mayincrease in width and/or cross-sectional area upon discharging. In yetanother embodiment, the change in the at least one dimension of themember of the population of cathode structures 112 uponexpansion/contraction of the members of the population of anodestructures 110 can be understood to generate an overall change in thecross-sectional area of the members of the population of cathodestructures 112 that is inversely related to a change in thecross-sectional areas of the members of the population of anodestructures. That is, in a case where members of the population of theanode structures 110 increase in cross-sectional area upon charging,members of the population of cathode structures 112 may decrease incross-sectional upon charging, and in a case where members of thepopulation of anode structures 110 decrease in cross-sectional area upondischarging, members of the population of cathode structures 112 mayincrease in cross-sectional area upon discharging. In yet anotherembodiment, the change in the at least one dimension of members of thepopulation of cathode structures 112 upon expansion/contraction ofmembers of the population of anode structures 110 can be understood togenerate an overall change in volume of the cathode structures 112 thatis inversely related to a change in volume of members of the populationof anode structures. That is, in a case where members of the populationof anode structures 110 increase in volume upon charging, members of thepopulation of cathode structures 112 may decrease in volume uponcharging, and in a case where members of the population of anodestructures 110 decrease in volume upon discharging, members of thepopulation of cathode structures 112 may increase in volume upondischarging.

Furthermore, in one embodiment, a sign of the change in the at least onedimension (e.g., the width), cross-section and/or volume of members ofthe population of cathode structures 112 is the opposite of that of asign of the change in the at least one dimension, cross-section and/orvolume of members of the population of anode structures 110, such thatthe change in sizes are inversely related to each other. For example,for a member of the population of anode structures 110 that increases inwidth upon charging of the secondary battery 102, a sign for the changein width would be the sign of the number resulting from subtraction ofthe initial width W_(I) from the final width W_(F), (W_(F)−W_(I)=+ΔW),which is a positive number with a positive sign (+) since W_(F) of theanode structure is greater than W_(I). Conversely, for a member of thepopulation of cathode structures 112 that decreases in width uponcharging of the secondary battery 102, a sign for the width change wouldbe W_(F)−W_(I)=−ΔW, which is a negative number with a negative sign (−)since W_(F) for the cathode structure is smaller than W_(I). However, itshould be noted that the absolute value of the magnitude of ΔW of theanode structure is not necessarily the same as the absolute value of themagnitude of ΔW for the cathode structure, during charge and/ordischarge. In other words, the extent of expansion of the anodestructure during charging does not have to equal the extent ofcontraction of the cathode structure. For example, other structures inthe secondary battery may at least partially accommodate the expansionof the anode structure, such that the compression of the cathodestructure is less than what might otherwise be expected if the cathodestructure were to compress to an extent to completely accommodate thefull extent of the anode structure expansion. The same may be true ofdischarging, where an extent of expansion of the cathode structure maybe of a different magnitude than the extent of contraction of the anodestructure during the discharge process. Thus, in a case where a memberof the population of anode structures 110 exhibits a change in width,cross-section and/or volume that has a positive sign (e.g., the widthincreases), the change in width, cross-section and/or volume of a memberof the population of cathode structures 112 may be inversely relatedthereto (although possibly of a different magnitude), and thus has anegative sign. Conversely, in a case where a member of the population ofanode structures exhibits a change in width, cross-section and/or volumethat has a negative sign (e.g., the width decreases), the change inwidth, cross-section and/or volume of a member of the population ofcathode structures 112 may be inversely related thereto (althoughpossibly of a different magnitude), and thus has a positive sign. Byproviding members of the population of cathode structures that arecapable of changing in at least one dimension, such as the width,cross-section and/or volume in relation to an expansion and/orcontraction of members of the population of anode structures, the strainon the electrode assembly 106 that can otherwise be caused by repeatedexpansion and contraction over multiple cycles of the secondary batterycan be reduced, thereby improving the lifetime and performance of thesecondary battery 102.

By way of further explanation, referring to FIGS. 2A-2C, an embodimentis shown of an electrode assembly 106 having members of the populationof cathode structures 110 that change size (e.g., width, cross-sectionalarea and/or volume) in relation to expansion/contraction of members ofthe population of anode structures 112, in both a charged state (FIGS.2A and 2C) and in a discharged state (FIG. 2B). In FIG. 2A showing acharged state for the secondary battery 102, the members of thepopulation of anode structure 110 have a cross-sectional area A₁ withwidth W_(A1), and members of the population of cathode structure 112have a cross-sectional area C₁ with width W_(C1). However, when thesecondary battery 102 is discharged to the discharged state shown inFIG. 2B, the width of members of the population of anode structures 110decreases to provide cross-sectional area A₂ and width W_(A2), while thewidth of members of the population of cathode structure 112 increases toprovide cross-sectional area C₂ an W_(C2), where A₂<A₁ and C₂>C₁, andW_(A2)<W_(A1) and W_(C2)>W_(C1). That is, the change in size of membersof the population of cathode structures 112 may be inversely related tothat of members of the population of anode structures 110, because thecathode structure population members increase in cross-sectional areaand/or width, while the anode structure population members decrease incross-sectional area and/or width, when the secondary battery isdischarged (the direction of the change in width is depictedschematically by the arrows in FIG. 2B). When the secondary battery 102is charged up from the discharged state shown in FIG. 2B to a subsequentcharged state shown in FIG. 2C, members of the population of anode andcathode structures 110, 112 exhibit a further change in cross-sectionalarea and/or width, with cross-sectional area of the members of thepopulation of anode structures increasing to A₃, where A₃<A₂, and thewidth of the members of the population of anode structures increasing toW_(A3), where W_(A3)>W_(A2), and the cross-sectional area of members ofthe population of cathode structures decreasing to C₃, where C₃<C₂, andthe width of members of the population of cathode structures decreasingto W_(C3), where W_(C3)<W_(C2). While in some embodiments thecross-sectional area A₃ and/or width W_(A3) of the members of thepopulation of anode structures 110 in the subsequent charged statedepicted in FIG. 2C may be the same as the corresponding cross-sectionalarea A₁ and/or width W_(A1) of the members of the population of anodestructures 110 in the initial charged state shown in FIG. 2A, it is alsopossible that the cross-sectional area A₃ and/or width W_(A3) of membersof the population of anode structures 110 in a subsequent charged statemay be increased over the cross-sectional area A1 and/or width W_(A1) ofmembers of the population of anode structure 110 in the initial chargedstate. That is, in certain embodiments, the width, cross-sectional areaand/or volume of members of the population of anode structures 110 inthe charged state may increase over repeated cycling of the secondarybattery 102 between charged and discharged states. Similarly, while thecross-sectional area C₃ and/or width W_(C3) of members of the populationof cathode structure 112 in the subsequent charged state depicted inFIG. 2C may be the same as the cross-sectional area C₃ and/or widthW_(C1) of the members of the population of cathode structures 112 in theinitial charged state depicted in 3A, it is also possible that thecross-sectional area C₃ and/or width W_(C3) of members of the populationof cathode structures 112 in a subsequent charged state may be decreasedover the corresponding cross-sectional area C₃ and/or width W_(C1) ofmembers of the population of cathode structures 112 in the initialcharged state. That is, in certain embodiments, the width,cross-sectional area and/or volume of the members of the population ofcathode structures 112 in the charged state may decrease over repeatedcycling of the secondary battery 102 between charged and dischargedstates, such as to accommodate an increase in growth of members of thepopulation of anode structures 110 that may occur over repeated cyclingof the secondary battery 102.

Accordingly, in one embodiment, members of the population of cathodestructures 112 have a first size, such as a first dimension and/orcross-sectional area when the secondary battery 102 is in the chargedstate, and have a second size, such as a second dimension and/orcross-sectional area when the secondary battery 102 is in the dischargedstate, with the first dimension and/or cross-sectional area being lessthan the second dimension and/or cross-sectional area. In yet anotherembodiment, the change in size, such as change in dimension and/orcross-sectional area of the cathode structures 112 may be inverselyrelated to a change in the dimension and/or cross-sectional area ofmembers of the population of anode structures 110. For example, in oneembodiment, at least one member of the population of cathode structures112 may have a first cross-sectional area C₁ in the charged state thatis no more than 3×10⁷ μm². By way of further example, in one embodimentat least one member of the population of cathode structures may have afirst cross-sectional area C₁ in the charged state that is no more than1×10⁷ μm². By way of further example, in one embodiment at least onemember of the population of cathode structures may have a firstcross-sectional area C₁ in the charged state that is no more than9.5×10⁶ μm². By way of yet further example, in one embodiment at leastone member of the population of cathode structure may have a firstcross-sectional area C₁ in the charged state that is no more than 8×10⁶μm². By way of yet further example, at least one member of population ofcathode structures may have a first cross-sectional area C₁ in thecharged state that is no more than 5×10⁶ μm². In general, the firstcross-sectional area C₁ of at least one member of the population ofcathode structures in the charged state may be at least 2×10² μm², forexample the first cross-sectional area C₁ in the charged state may be atleast 2.5×10² μm², and even at least 3×10² μm². For example, the firstcross-sectional area C₁ may be in the range of from 2×10² μm² to 3×10⁷μm², such as from 2.5×10² μm² to 9.5×10⁶ μm², and even in the range offrom 3×10² μm² to 8×10⁶ μm².

Furthermore, in one embodiment, at least one member of the population ofcathode structures have a second cross-sectional area C₂ in thedischarged state that is at least 1.01×10² μm². By way of furtherexample, in one embodiment at least one member of the population ofcathode structures may have a second cross-sectional area C₂ in thedischarged state that is at least 1.05×10² μm². By way of furtherexample, in one embodiment at least one member of the population ofcathode structures may have a second cross-sectional area C₂ in thedischarged state that is at least 1.0×10³ μm². By way of furtherexample, in one embodiment at least one member of the population ofcathode structures may have a second cross-sectional area C₂ in thedischarged state that is at least 1.05×10³ μm². By way of furtherexample, in one embodiment at least one member of the population ofcathode structures may have a second cross-sectional area C₂ in thedischarged state that is at least 1.1×10³ μm². In general, the secondcross-sectional area C₂ of at least one member of the population ofcathode structures in the charged state will not exceed 1.5×10¹⁰, forexample the second cross-sectional area C₂ in the discharged state maynot exceed 1×10⁷ μm², and even may not exceed 1×10⁶ μm². For example,the second cross-sectional area C₂ may be in the range of from 1.01×10²μm² to 1.5×10¹⁰ μm², such as from 1.0×10³ μm² to 1.0×10⁷ μm², and evenin the range of from 1.05×10² μm^(t) to 1×10⁶ μm².

In yet another embodiment, in one embodiment at least one member of thepopulation of cathode structures has a ratio of the secondcross-sectional area C₂ of the cathode structure 112 in the dischargedstate to a first cross-sectional area C₁ of the cathode structure 112 inthe charged state that is at least 1.05:1. By way of further example, inone embodiment at least one member of the population of cathodestructures has a ratio of the second cross-sectional area C₂ of thecathode structure 112 to the first cross-sectional area C₁ of thecathode structure 112 that is at least 1.1:1. By way of further example,in one embodiment at least one member of the population of cathodestructures has a ratio of the second cross-sectional area C₂ of thecathode structure 112 to the first cross-sectional area C₁ of thecathode structure 112 that is at least 1.3:1. By way of further example,in one embodiment at least one member of the population of cathodestructures has a ratio of the second cross-sectional area C₂ of thecathode structure 112 to the first cross-sectional area C1 of thecathode structure 112 that is at least 2:1. By way of further example,in one embodiment at least one member of the population of cathodestructures has a ratio of the second cross-sectional area C₂ of thecathode structure 112 to the first cross-sectional area C1 of thecathode structure 112 that is at least 3:1. By way of further example,in one embodiment at least one member of the population of cathodestructures has a ratio of the second cross-sectional area C₂ of thecathode structure 112 to the first cross-sectional area C1 of thecathode structure 112 that is at least 4:1. By way of further example,in one embodiment at least one member of the population of cathodestructures has a ratio of the second cross-sectional area C₂ of thecathode structure 112 to the first cross-sectional area C₁ of thecathode structure 112 that is at least 6:1. Generally, the ratio of thesecond cross-sectional area C2 to the first cross-sectional area C1 willnot exceed about 15:1, and will even not exceed 10:1, such as forexample not exceeding 8:1. For example, in one embodiment at least onemember of the population of cathode structures has a ratio of the secondcross-sectional area C₂ of the cathode structure 112 to the firstcross-sectional area C₁ of the cathode structure 112 that may be in therange of from 1.05:1 to 15:1. By way of further example, in oneembodiment at least one member of the population of cathode structureshas a ratio of the second cross-sectional area C₂ of the cathodestructure 112 to the first cross-sectional area C1 of the cathodestructure 112 that may be in the range of from 1.1:1 to 6:1. By way offurther example, in one embodiment at least one member of the populationof cathode structures has a ratio of the second cross-sectional area C₂of the cathode structure 112 to the first cross-sectional area C₁ of thecathode structure 112 that may be in the range of from 1.3:1 to 4:1.Furthermore, in one embodiment, the contraction of first cross-sectionalarea C₁ with respect to the second cross-sectional area C₂ is in therange of from 2% contraction to 90% contraction, such as from 5%contraction to 75% contraction. That is, the first cross-sectional areaC₁ may be contracted by at least 2% with respect to C₂, such as at least5% and even at least 10% with respect to C₂, but may be contracted lessthan 90% with respect to C₂, such as less than 80% and even less than75% with respect to C₂.

Furthermore, in one embodiment, at least one member of the population ofanode structures 110 may have a first cross-sectional area A₁ in thecharged state that is at least 100 μm². By way of further example, inone embodiment at least one member of the population of anode structuresmay have a first cross-sectional area A₁ in the charged state that is atleast 1×10³ μm². By way of yet further example, in one embodiment atleast one member of the population of anode structures may have a firstcross-sectional area A₁ in the charged state that is at least 4.5×10³μm². By way of yet further example, at least one member of population ofanode structures may have a first cross-sectional area A₁ in the chargedstate that is at least 6×10³ μm². By way of further example, in oneembodiment at least one member of the population of anode structures mayhave a first cross-sectional area A₁ in the charged state that is atleast 8×10³ μm². In general, the first cross-sectional area A₁ of atleast one member of the population of anode structures in the chargedstate may not exceed 1.5×10⁷ μm², for example the first cross-sectionalarea A₁ in the charged state may not exceed 7.6×10⁶ μm², and may evennot exceed 5×10⁶ μm². For example, the first cross-sectional area A₁ maybe in the range of from 100 μm² to 1.5×10⁷ μm², such as from 4.5×10³ μm²to 7.6×10⁶ μm², and even in the range of from 6×10³ μm² to 5×10⁶ μm².

Furthermore, in one embodiment, at least one member of the population ofanode structures have a second cross-sectional area A₂ in the dischargedstate that is no more than 3×10⁷ μm². By way of further example, in oneembodiment at least one member of the population of anode structures mayhave a second cross-sectional area A₂ in the discharged state that is nomore than 1.5×10⁷ μm². By way of further example, in one embodiment atleast one member of the population of anode structures may have a secondcross-sectional area A₂ in the discharged state that is no more than7.5×10⁶ μm². By way of further example, in one embodiment at least onemember of the population of anode structures may have a secondcross-sectional area A₂ in the discharged state that is no more than5×10⁶ μm². By way of further example, in one embodiment at least onemember of the population of anode structures may have a secondcross-sectional area A₂ in the discharged state that is no more than3×10⁶ μm². In general, the second cross-sectional area A₂ of at leastone member of the population of anode structures in the charged statewill be at least 500 μm², for example the second cross-sectional area A₂in the discharged state may be at least 1.5×10³, and even at least 3×10³μm². For example, the second cross-sectional area A₂ may be in the rangeof from 500 μm² to 3×10⁷ μm², such as from 1.5×10³ μm² to 7.5×10⁶ μm²,and even in the range of from 3×10³ μm² to 5×10⁶ μm².

In yet another embodiment, in one embodiment at least one member of thepopulation of anode structures has a ratio of the first cross-sectionalarea A₁ of the anode structure 110 in the charged state to a secondcross-sectional area A₂ of the anode structure 110 in the dischargedstate that is at least 1.01:1. By way of further example, in oneembodiment at least one member of the population of anode structures hasa ratio of the first cross-sectional area A₁ of the anode structure 110to the second cross-sectional area A₂ of the anode structure 110 that isat least 1.05:1. By way of further example, in one embodiment at leastone member of the population of anode structures has a ratio of thefirst cross-sectional area A₁ of the anode structure 110 to the secondcross-sectional area A₂ of the anode structure 110 that is at least1.5:1. By way of further example, in one embodiment at least one memberof the population of anode structures has a ratio of the firstcross-sectional area A₁ of the anode structure 110 to the secondcross-sectional area A₂ of the anode structure 110 that is at least 2:1.By way of further example, in one embodiment at least one member of thepopulation of anode structures has a ratio of the first cross-sectionalarea A₁ of the anode structure 110 to the second cross-sectional area A₂of the anode structure 110 that is at least 3:1. By way of furtherexample, in one embodiment at least one member of the population ofanode structures has a ratio of the first cross-sectional area A₁ of theanode structure 110 to the second cross-sectional area A₂ of the anodestructure 110 that is at least 4:1. By way of further example, in oneembodiment at least one member of the population of anode structures hasa ratio of the first cross-sectional area A₁ of the anode structure 110to the second cross-sectional area A₂ of the anode structure 110 that isat least 5:1. For example, in one embodiment at least one member of thepopulation of anode structures has a ratio of the first cross-sectionalarea A₁ of the anode structure 110 to the second cross-sectional area A₂of the anode structure 110 that may be in the range of from 1.01:1 to5:1. By way of further example, in one embodiment at least one member ofthe population of anode structures has a ratio of the firstcross-sectional area A₁ of the anode structure 110 to the secondcross-sectional area A₂ of the anode structure 110 that may be in therange of from 1.01 to 4:1. By way of further example, in one embodimentat least one member of the population of anode structures has a ratio ofthe first cross-sectional area A₁ of the anode structure 110 to thesecond cross-sectional area A₂ of the anode structure 110 that may be inthe range of from 1.01:1 to 3:1, and even in the range of from 1.5:1 to3:1.

In one embodiment, a subset of the anode structure population has amedian cross-sectional area, as measured either according to MA_(A),which as used herein refers to a median of cross-sectional areas formore than one anode member, and/or according to ML_(A), which as usedherein refers to a median of cross-sectional areas at differentlongitudinal planes long an anode member, and/or according to MO_(A),which are used herein refers to a median of MA_(A) and ML_(A).Furthermore, a subset of the cathode structure population has a mediancross-sectional area, as measured either according to MA_(C), which asused herein refers to a median of cross-sectional areas for more thanone cathode member, and/or according to ML_(C), which as used hereinrefers to a median of cross-sectional areas at different longitudinalplanes long a cathode member, and/or according to MO_(C), which are usedherein refers to a median of MA_(C) and ML_(C). Further description ofthese measures are as follows.

According to one embodiment, a subset of the anode structure populationhas a median cross-sectional area MA_(A), and a subset of the cathodestructure population has a median cross-sectional area MA_(C), whereMA_(A) and MA_(C) are the medians of the cross-sectional areas A and Cfor members of the population of anode structures and cathode structuresrespectively, as measured across a subset of the anode and/or cathodestructure population. That is, MA_(A) can be understood as the mediancross-section as measured in the first longitudinal plane 113 for asubset of members of the population of anode structures, and MA_(C) canbe understood as the median cross-section as measured in the firstlongitudinal plane 113 for a subset of members of the population ofcathode structures. That is, to determine the median cross-sectionalarea MA_(A) for the subset, the cross-sectional areas are determined foreach member of the anode structure population in the subset, and thenthe median of the cross-sectional areas are evaluated. Similarly, todetermine the median cross-sectional area MA_(C) for the subset, thecross-sectional areas are determined for each member of the cathodestructure population in the subset, and then the median of thecross-sectional areas are evaluated. In one embodiment, the median ofthe cross-sectional areas as measured in the first longitudinal planeare determined for a subset comprising at least two members. In anotherembodiment, the median of the cross-sectional areas as measured in thefirst longitudinal plane are determined for a subset comprising at leastfive members. In another embodiment, the median of the cross-sectionalareas as measured in the first longitudinal plane are determined for asubset comprising at least ten members. In another embodiment, themedian of the cross-sectional areas as measured in the firstlongitudinal plane are determined for a subset comprising at least 20members. In another embodiment, the median of the cross-sectional areasas measured in the first longitudinal plane are determined for a subsetcomprising at least 50 members. For example, in one embodiment, thesubset of the population can comprise from 1 to 7 members, such as from2 to 6 members, and even from 3 to 5 members. In yet another embodiment,the subset of the population can comprise a percentage of the totalnumber of members in the electrode assembly 106. For example, the subsetcan comprise at least 10% of the members in the electrode assembly, suchas at least 25% of the members, and even at least 50%, such as at least75%, and even at least 90% of the members in the electrode assembly.

In one embodiment, the subset of the population of cathode structures112 may have a first median cross-sectional area MA_(C1) in the chargedstate that may be the same as and/or similar to values give above forthe first cross-sectional area C₁ of a member of the population ofcathode structures in the charged state. For example, in one embodiment,the subset of the population of cathode structures 112 may have a firstmedian cross-sectional area MA_(C1) that is no more than 3×10⁷ μm². Byway of further example, in one embodiment, the subset of the populationof cathode structures 112 may have a first median cross-sectional areaMA_(C1) in the charged state that is no more than 1×10⁷ μm². By way ofyet further example, in one embodiment the subset of the population ofcathode structures 112 may have a first median cross-sectional areaMA_(C1) in the charged state that is no more than 9.03×10⁶ μm². By wayof yet further example, in one embodiment, the subset of the populationof cathode structures 112 may have a first median cross-sectional areaMA_(C1) in the charged state that is no more than 8×10⁶ μm². By way offurther example, in one embodiment the subset of the population ofcathode structures 112 may have a first median cross-sectional areaMA_(C1) in the charged state that is no more than 5×10⁶ μm². In general,the first median cross-sectional area MA_(C1) of the subset of thepopulation of cathode structure may be at least 2×10² μm², for examplethe first median cross-sectional area MA_(C1) of the subset of thepopulation of cathode structures may be at least 2.6×10² μm², forexample the first median cross-sectional area MA_(C1) in the chargedstate may be at least 3×10² μm². For example, the first mediancross-sectional area MA_(C1) may be in the range of from 1×10² μm² to3×10⁷ μm², such as from 2.6×10² μm² to 9.03×10⁶ μm², and even in therange of from 3×10² μm² to 8×10⁶ μm².

Furthermore, in one embodiment, the subset of the population of cathodestructures 112 may have a second median cross-sectional area MA_(C2) inthe discharged state that may be the same as and/or similar to valuesgive above for the second cross-sectional area C₂ of a member of thepopulation of cathode structures in the discharged state. For example,in one embodiment, the subset of the population of cathode structures112 may have a second median cross-sectional area MA_(C2) in the chargedstate in the discharged state that is at least 1.01×10² μm². By way offurther example, in one embodiment the subset of the population ofcathode structures 112 may have a second median cross-sectional areaMA_(C2) in the discharged state that is at least 1.05×10² μm². By way offurther example, in one embodiment the subset of the population ofcathode structures 112 may have a second median cross-sectional areaMA_(C2) in the discharged state that is at least 1.05×10³ μm². By way offurther example, the subset of the population of cathode structures 112may have a second median cross-sectional area MA_(C2) in the dischargedstate that is at least 1.1×10³ μm². By way of further example, thesubset of the population of cathode structures 112 may have a secondmedian cross-sectional area MA_(C2) in the discharged state that is atleast 1.5×10³ μm². In general, the second median cross-sectional areaMA_(C2) of the subset of the population of cathode structures in thedischarged state will not exceed 1.5×10¹⁰ μm², for example the secondmedian cross-sectional area MA_(C2) in the discharged state may notexceed 9.5×10⁶ μm², and may even not exceed 1×10⁶ μm² For example, thesecond median cross-sectional area MA_(C2) may be in the range of from1.01×10² μm² to 1.5×10¹⁶ μm², such as from 1.05×10³ μm² to 9.5×10⁶ μm²,and even in the range of from 1.1×10² μm² to 1×10⁶ μm².

In yet another embodiment, the subset of the population of cathodestructures 112 may have a ratio of the second median cross-sectionalarea MA_(C2) in the discharged state to a first median cross-sectionalarea MA_(C1) in the charged state that is the same as and/or similar tothe values given above for the ratio of the second cross-sectional areaC₂ in the discharged state to the first cross-sectional area C₁ in thecharged state. For example, in one embodiment the subset of thepopulation of cathode structures has a ratio of the second mediancross-sectional area MA_(c2) in the discharged state to a first mediancross-sectional area MA_(c1) in the charged state that is at least1.05:1. By way of further example, in one embodiment the subset of thepopulation of cathode structures has a ratio of the second mediancross-sectional area MA_(c2) in the discharged state to a first mediancross-sectional area MA_(c1) in the charged state that is at least1.1:1. By way of further example, in one embodiment the subset of thepopulation of cathode structures has a ratio of the second mediancross-sectional area MA_(c2) in the discharged state to a first mediancross-sectional area MA_(c1) in the charged state that is at least1.3:1. By way of further example, in one embodiment the subset of thepopulation of cathode structures has a ratio of the second mediancross-sectional area MA_(c2) in the discharged state to a first mediancross-sectional area MA_(c1) in the charged state that is at least 2:1.By way of further example, in one embodiment the subset of thepopulation of cathode structures has a ratio of the second mediancross-sectional area MA_(c2) in the discharged state to a first mediancross-sectional area MA_(c1) in the charged state that is at least 3:1.By way of further example, in one embodiment the subset of thepopulation of cathode structures has a ratio of the second mediancross-sectional area MA_(c2) in the discharged state to a first mediancross-sectional area MA_(c1) in the charged state that is at least 4:1.By way of further example, in one embodiment the subset of thepopulation of cathode structures has a ratio of the second mediancross-sectional area MA_(c2) in the discharged state to a first mediancross-sectional area MA_(c1) in the charged state that is at least 6:1.Generally, a ratio of MA_(c2) to MA_(c1) for the subset will not exceedabout 15:1 and will even not exceed 10:1, such as for example notexceeding 8:1. For example, the subset of the population of cathodestructures has a ratio of the second median cross-sectional area MA_(c2)in the discharged state to a first median cross-sectional area MA_(c1)in the charged state that may be in the range of from 1.05:1 to 15:1. Byway of further example, the subset of the population of cathodestructures has a ratio of the second median cross-sectional area MA_(c2)in the discharged state to a first median cross-sectional area MA_(c1)in the charged state that may be in the range of from 1.1:1 to 6:1. Byway of further example, in one embodiment the subset of the populationof cathode structures has a ratio of the second median cross-sectionalarea MA_(c2) in the discharged state to a first median cross-sectionalarea MA_(c1) in the charged state that may be in the range of from 1.3:1to 4:1. By way of further example, in one embodiment the contraction ofthe subset of the first median cross-sectional area MA_(C1) with respectto the second median cross-sectional area MA_(C2) may be in the range offrom 2% contraction to 90% contraction, such as from 5% contraction to75% contraction. That is, the subset of the population of cathodestructures may have a first median cross-sectional area MA_(C1) that iscontracted by at least 2% with respect to the second mediancross-sectional area MA_(C2), such as at least 5% and even at least 10%with respect to the second median cross-sectional area MA_(C2), but maybe contracted less than 90% with respect to the second mediancross-sectional area MA_(C2), such as less than 80% and even less than75% with respect to the second median cross-sectional area MA_(C2).

Furthermore, in one embodiment, the subset of the population of anodestructures 110 may have a first median cross-sectional area MA_(A1) inthe charged state that may be the same as and/or similar to values giveabove for the first cross-sectional area A₁ of a member of thepopulation of anode structures in the charged state. For example,according to one embodiment, the subset of the population of anodestructures 110 may have a first median cross-sectional area MA_(A1) inthe charged state that is at least 100 μm². By way of further example,in one embodiment the subset of the population of anode structures 110may have a first median cross-sectional area MA_(A1) in the chargedstate that is at least 1×10³ μm². By way of yet further example, in oneembodiment the subset of the population of anode structures 110 may havea first median cross-sectional area MA_(A1) in the charged state that isat least 4.7×10³ μm². By way of yet further example, the subset of thepopulation of anode structures 110 may have a first mediancross-sectional area MA_(A1) in the charged state that is at least 6×10³μm². By way of further example, in one embodiment the subset of thepopulation of anode structures 110 may have a first mediancross-sectional area MA_(A1) in the charged state that is at least 8×10³μm². In general, the first median cross-sectional area MA_(A1) of thesubset of the population of anode structures in the charged state maynot exceed 1.5×10⁷ μm², for example the first median cross-sectionalarea MA_(A1) in the charged state may not exceed 6.8×10⁷ μm², and maynot even exceed 5×10⁶ μm². For example, the first median cross-sectionalarea MA_(A1) in the charged state may be in the range of from 100 μm² to1.5×10⁷ μm², such as from 4.7×10³ μm² to 6.8×10⁶ μm², and even in therange of from 6×10³ μm² to 5×10⁶ μm².

Furthermore, in one embodiment, the subset of the population of anodestructures 110 may have a second median cross-sectional area MA_(A2) inthe discharged state that may be the same as and/or similar to valuesgive above for the second cross-sectional area A₂ of a member of thepopulation of anode structures in the discharged state. For example, inone embodiment, the subset of the population of anode structures 110 mayhave a second median cross-sectional area MA_(A2) in the dischargedstate that is no more than 3×10⁷ μm². By way of further example, in oneembodiment the subset of the population of anode structures 110 may havea second median cross-sectional area MA_(A2) in the discharged statethat is no more than 1.5×10⁷ μm². By way of further example, in oneembodiment the subset of the population of anode structures 110 may havea second median cross-sectional area MA_(A2) in the discharged statethat is no more than 7.1×10⁶ μm². By way of further example, in oneembodiment the subset of the population of anode structures 110 may havea second median cross-sectional area MA_(A2) in the discharged statethat is no more than 5×10⁶ μm². By way of further example, in oneembodiment the subset of the population of anode structures 110 may havea second median cross-sectional area MA_(A2) in the discharged statethat is no more than 3×10⁶ μm². In general, the second mediancross-sectional area MA_(A2) of the subset of the population of anodestructures in the charged state will be at least 1.5×10³ μm², forexample the second median cross-sectional area MA_(A2) in the dischargedstate may be at least 1.6×10³ μm², and even at least 3×10³ μm². Forexample, the second median cross-sectional area MA_(A2) in thedischarged state may be in the range of from 500 μm² to 3×10⁷ μm², suchas from 1.6×10³ μm² to 7.1×10⁶ μm², and even in the range of from 3×10³μm² to 5×10⁶ μm².

In yet another embodiment, the subset of the population of anodestructures 110 may have a ratio of the first median cross-sectional areaMA_(A1) in the charged state to a second median cross-sectional areaMA_(A2) in the discharged state that is the same as and/or similar tothe values given above for the ratio of the first cross-sectional areaA₁ in the charged state to the second cross-sectional area A₂ in thedischarged state. For example, in one embodiment the subset of thepopulation of anode structures has a ratio of the first mediancross-sectional area MA_(A1) in the charged state to a second mediancross-sectional area MA_(A2) in the discharged state that is at least1.01:1. By way of further example, in one embodiment the subset of thepopulation of anode structures has a ratio of the first mediancross-sectional area MA_(A1) in the charged state to a second mediancross-sectional area MA_(A2) in the discharged state that is at least1.05:1. By way of further example, in one embodiment the subset of thepopulation of anode structures has a ratio of the first mediancross-sectional area MA_(A1) in the charged state to a second mediancross-sectional area MA_(A2) in the discharged state that is at least1.5:1. By way of further example, in one embodiment the subset of thepopulation of anode structures has a ratio of the first mediancross-sectional area MA_(A1) in the charged state to a second mediancross-sectional area MA_(A2) in the discharged state that is at least2:1. By way of further example, in one embodiment the subset of thepopulation of anode structures has a ratio of the first mediancross-sectional area MA_(A1) in the charged state to a second mediancross-sectional sectional area MA_(A2) in the discharged state that isat least 3:1. By way of further example, in one embodiment the subset ofthe population of anode structures has a ratio of the first mediancross-sectional area MA_(A1) in the charged state to a second mediancross-sectional area MA_(A2) in the discharged state that is at least4:1. By way of further example, in one embodiment the subset of thepopulation of anode structures has a ratio of the first mediancross-sectional area MA_(A1) in the charged state to a second mediancross-sectional area MA_(A2) in the discharged state that is at least5:1. For example, in one embodiment the subset of the population ofanode structures has a ratio of the first median cross-sectional areaMA_(A1) in the charged state to a second median cross-sectional areaMA_(A2) in the discharged state that may be the range of from 1.01:1 to5:1. By way of further example, in one embodiment the subset of thepopulation of anode structures has a ratio of the first mediancross-sectional area MA_(A1) in the charged state to a second mediancross-sectional area MA_(A2) in the discharged state that may be in therange of from 1.01 to 4:1. By way of further example, in one embodimentthe subset of the population of anode structures has a ratio of thefirst median cross-sectional area MA_(A1) in the charged state to asecond median cross-sectional area MA_(A2) in the discharged state thatmay be in the range of from 1.01:1 to 3:1, and even in the range of from1.5:1 to 3:1.

In yet another embodiment, the members of the population of anodestructures can each be understood to have a length L_(A) measured in thetransverse direction, a width W_(A) measured in the longitudinaldirection, and a height H_(A) measured in the vertical direction, asshown for example in FIG. 1A. Similarly, the members of the populationof cathode structures can each be understood to have a length L_(C)measured in the transverse direction, a width W_(C) measured in thelongitudinal direction, and a height H_(C) measured in the verticaldirection. The lengths L_(A) and L_(C) of the anode and cathodestructure members, respectively, may be as measured from a bottom 115 aof each member to a top 115 b, as depicted for example in FIG. 1C, wherethe bottom 115 a is proximate to a plane 121 from which the memberextends, and the top 115 b is distal to the plane 121. Furthermore, inone embodiment, the length L_(A) and/or L_(C) of members of thepopulation of anode and/or cathode structures may be at least 5 timeseach of the width and the height of the members (e.g., the length of themember may be the longer than either the width or the height). Forexample, a ratio of the length L (e.g., either L_(A) or L_(C)) ofmembers to each of the width W (e.g., either W_(A) or W_(C)) and theheight H (e.g., either H_(A) or H_(C)), may be at least 10:1, and evenat least 15:1, such as at least 20:1.

According to one aspect, the cross-sectional area of the at least onemember of the cathode and/or anode populations is measured in a firstlongitudinal plane that is not only parallel to the longitudinaldirection, but is also orthogonal to the direction of one or more of thedirection of L_(A) and L_(C). For example, referring to the embodimentin FIG. 1C, the first longitudinal plane 113 is depicted as beingparallel with the stacking direction (longitudinal direction), whilealso being perpendicular to the length direction of the members of theanode and cathode structure populations, which is the X direction asdepicted in the embodiment therein. For example, according to oneembodiment, the first longitudinal plane may be in a Z-Y plane, where Ycorresponds to an axis that is parallel to the longitudinal direction,and Z corresponds to an axis that is orthogonal to the longitudinaldirection while also being orthogonal to the lengths L_(A) and/or L_(C)of the members of the population of anode structures and cathodestructures, respectively. In yet another embodiment, the firstlongitudinal plane in which the cross-sectional area(s) are measured isin a plane that is less than 15 degrees away from the Z-Y plane asrotated along the Y axis (e.g., longitudinal axis). In yet anotherembodiment, the first longitudinal plane in which the cross-sectionalarea(s) are measured is in a plane that is less than 45 degrees awayfrom the Z-Y plane as rotated along the Y axis (e.g., longitudinalaxis). In yet another embodiment, the first longitudinal plane in whichthe cross-sectional area(s) are measured is in a plane that is greaterthan 45 degrees away from the Z-Y plane but less than 90 degrees fromthe Z-Y plane as rotated along the Y axis (e.g., longitudinal axis). Inyet another embodiment, the first longitudinal plane is in an X-Y plane,where the Y-axis corresponds to an axis that the parallel to thelongitudinal direction, and the X-axis corresponds to an axis that isorthogonal to the longitudinal axis, and that is also parallel to thelengths L_(A) and/or L_(C) of the members of the population of anodestructures and cathode structures, respectively. Furthermore, in oneembodiment, the position of the first longitudinal plane 113 along thelength L_(A) or L_(C) of the anodes and/or cathodes may be selectedaccording to the measurement to be made. For example, in one embodiment,the first longitudinal plane 113 may be positioned in the Z-Y planeabout half-way along the length L of the anodes and/or cathodes (e.g.,about half-way along the length in the X-direction), as depicted in FIG.1C. In another embodiment, the first longitudinal plane may bepositioned in the Z-Y plane closer to an end of one or more of thecathode and/or anode structures (e.g., closer to the base or top of theanodes and/or cathodes in the X-direction). In yet another embodiment,cross-sectional areas can be measured in a plurality of longitudinalplanes 113 a, 113 b that are parallel to the longitudinal direction.

According to yet another embodiment, at least one member of a subset ofthe anode structure population can have a median cross-sectional areaML_(A) that is the median for the member of a plurality ofcross-sectional areas A as measured in a plurality of planes parallel tothe longitudinal direction for that member. Similarly, at least onemember of a subset of the cathode population can have a mediancross-sectional area ML_(C) that is the median for the member of aplurality of cross-sectional areas C as measured in a plurality ofplanes parallel to the longitudinal direction for that member. Forexample, referring to FIG. 1C, the cross-sections A for a member of thepopulation of anode structures may be measured in a plurality of planes113 a,b parallel to the longitudinal direction for that member, such asfor example the first longitudinal plane 113 and one or more planes 113a,b. In one embodiment, the one or more other planes 113 a,b are planesthat are parallel to the first longitudinal plane 113, and may belocated at different positions along the length of the anodes (e.g., atdifferent positions on the X-axis). The median cross-sectional areaML_(A) may thus be calculated as the median of the cross-sections Ameasured in each longitudinal plane for the member of the population ofanode structures. Similarly, the cross-sections C for a member of thepopulation of cathode structures may be measured in a plurality ofplanes 113 a,b parallel to the longitudinal direction for that member,such as for example the first longitudinal plane 113 and one or moreplanes 113 a,b. In one embodiment, the one or more other planes 113 a,bare planes that are parallel to the first longitudinal plane 113, andmay be located at different positions along the length of the cathodes(e.g., at different positions on the X-axis). The median cross-sectionalare ML_(C) may thus be calculated as the median of the cross-sections Cmeasured in each longitudinal plane for the member of the population ofcathode structures.

In one embodiment, the median cross-sectional areas ML_(A) and ML_(C)are the median cross-sectional areas of the cross-sectional areas asmeasured in at least two longitudinal planes for the anode and cathodestructure population subsets, respectively. In one embodiment, themedian cross-sectional areas ML_(A) and ML_(C) are the mediancross-sectional areas of the cross-sectional areas as measured in atleast three longitudinal planes for the anode and cathode structurepopulation subsets, respectively. In one embodiment, the mediancross-sectional areas ML_(A) and ML_(C) are the median cross-sectionalareas of the cross-sectional areas as measured in at least fivelongitudinal planes for the anode and cathode structure populationsubsets, respectively. In one embodiment, the median cross-sectionalareas ML_(A) and ML_(C) are the median cross-sectional areas of thecross-sectional areas as measured in at least ten longitudinal planesfor the anode and cathode structure population subsets, respectively.Furthermore, in one embodiment, the median cross-sectional areas M_(LA)and M_(LC) may be the median of cross-sectional areas as measured in atleast two longitudinal planes that are distanced apart from each otherby a predetermined length. For example, in one embodiment, the mediancross-sectional areas M_(LA) and M_(LC) are the median ofcross-sectional areas as measured for a member in at least twolongitudinal planes that are spaced apart from one another by at least10% of the length L_(A) and/or L_(C) of the members (e.g., spaced apartalong the X-axis). As another example, in one embodiment, the mediancross-sectional areas M_(LA), and M_(LC) are the median ofcross-sectional areas as measured for a member in at least twolongitudinal planes that are spaced apart from one another by at least15% of the length L_(A) and/or L_(C) of the members (e.g., spaced apartalong the X-axis). As another example, in one embodiment, the mediancross-sectional areas M_(LA), and M_(LC) are the median ofcross-sectional areas as measured for a member in at least twolongitudinal planes that are spaced apart from one another by at least20% of the length L_(A) and/or L_(C) of the members (e.g., spaced apartalong the X-axis). For example, in one embodiment, the mediancross-sectional areas M_(LA) and M_(LC) are the median ofcross-sectional areas as measured for a member in at least twolongitudinal planes that are spaced apart from one another by at least25% of the length L_(A) and/or L_(C) of the members (e.g., spaced apartalong the X-axis). As another example, in one embodiment, the mediancross-sectional areas M_(LA), and M_(LC) are the median ofcross-sectional areas as measured for a member in at least twolongitudinal planes that are spaced apart from one another by at least30% of the length L_(A) and/or L_(C) of the members (e.g., spaced apartalong the X-axis). As another example, in one embodiment, the mediancross-sectional areas M_(LA), and M_(LC) are the median ofcross-sectional areas as measured for a member in at least twolongitudinal planes that are spaced apart from one another by at least50% of the length L_(A) and/or L_(C) of the members (e.g., spaced apartalong the X-axis). As another example, in one embodiment, the mediancross-sectional areas M_(LA), and M_(LC) are the median ofcross-sectional areas as measured for a member in at least twolongitudinal planes that are spaced apart from one another by at least75% of the length L_(A) and/or L_(C) of the members (e.g., spaced apartalong the X-axis).

Accordingly, in one embodiment, at least one member of the anodestructure population subset may have a first median cross-sectional areaML_(A1) when the secondary battery is in the charged state, and a secondmedian cross-sectional area ML_(A2) when the secondary battery is in thedischarged state, and similarly at least one member of the cathodestructure population subset may have a first median cross-sectional areaML_(C1) when the secondary battery is in the charged state, and a secondmedian cross-sectional area ML_(C2) when the secondary battery is in thedischarged state, where ML_(A1) is greater than ML_(A2) for each of themembers of the subset of the anode structure population, and ML_(C1) isless than ML_(C2) for each of the members of the subset of the cathodepopulation.

In one embodiment, at least one member of the subset of the populationof cathode structures 112 may have a first median cross-sectional areaML_(c1) in the charged state that may be the same as and/or similar tovalues given above for the first cross-sectional area C₁ of a member ofthe population of cathode structures in the charged state. For example,in one embodiment, the at least one member of the subset of thepopulation of cathode structures 112 may have a first mediancross-sectional area ML_(C1) in the charged state that is no more than3×10⁷ μm². By way of further example, in one embodiment, the at leastone member of the subset of the population of cathode structures 112 mayhave a first median cross-sectional area ML_(C1) in the charged statethat is no more than 1×10⁷ μm². By way of yet further example, in oneembodiment the at least one member of the subset of the population ofcathode structures 112 may have a first median cross-sectional areaML_(C1) in the charged state that is no more than 9.03×10⁶ μm². By wayof yet further example, in one embodiment, the at least one member ofthe subset of the population of cathode structures 112 may have a firstmedian cross-sectional area ML_(C1) in the charged state that no morethan 8×10⁶ μm². By way of further example, in one embodiment the atleast one member of the subset of the population of cathode structures112 may have a first median cross-sectional area ML_(C1) in the chargedstate that is no more than 5×10⁶ μm². In general, the first mediancross-sectional area ML_(C1) of the at least one member of the subset ofthe population of cathode structures may be at least 2×10² μm², forexample the first median cross-sectional area ML_(C1) in the chargedstate may be at least 2.6×10² μm², and even at least 3×10² μm². Forexample, the first median cross-sectional area ML_(C1) in the chargedstate may be in the range of from 1×10² μm² to 3×10⁷ μm², such as from2.6×10² μm² to 9.03×10⁶ μm², and even in the range of from 3×10² μm² to8×10⁶ μm².

Furthermore, in one embodiment, at least one member of the subset of thepopulation of cathode structures 112 may have a second mediancross-sectional area ML_(c2) in the discharged state that may be thesame as and/or similar to values give above for the secondcross-sectional area C₂ of a member of the population of cathodestructures in the discharged state. For example, in one embodiment, atleast one member of the subset of the population of cathode structures112 may have a second median cross-sectional area ML_(C2) in thedischarged state that is at least 1.01×10² μm². By way of furtherexample, in one embodiment the at least one member of the subset of thepopulation of cathode structures 112 may have a second mediancross-sectional area ML_(C2) in the discharged state that is at least1.05×10² μm². By way of further example, in one embodiment the at leastone member of the subset of the population of cathode structures 112 mayhave a second median cross-sectional area ML_(C2) in the dischargedstate that is at least 1.05×10³ μm². By way of further example, the atleast one member of the subset of the population of cathode structures112 may have a second median cross-sectional area ML_(C2) in thedischarged state that is at least 1.1×10³ μm². By way of furtherexample, in one embodiment the at least one member of the subset of thepopulation of cathode structures 112 may have a second mediancross-sectional area ML_(C2) in the discharged state that is at least1.5×10³ μm². In general, the second median cross-sectional area ML_(c2)of the at least one member of the subset of the population of cathodestructures in the discharged state will not exceed 1.5×10¹⁰ μm², forexample the second median cross-sectional area MA_(c2) in the dischargedstate of the at least one member may not exceed 9.5×10⁶ μm², and evenmay not exceed 1×10⁶ μm². For example, the second median cross-sectionalarea ML_(C2) may be in the range of from 1.01×10² μm² to 1.5×10¹⁰ μm²,such as from 1.05×10³ μm² to 9.5×10⁶ μm², and even in the range of from1.1×10² μm² to 1×10⁶ μm².

In yet another embodiment, at least one member of the subset of thepopulation of cathode structures 112 may have a ratio of the secondmedian cross-sectional area ML_(C2) in the discharged state to a firstmedian cross-sectional area ML_(C1) in the charged state that is thesame as and/or similar to the values given above for the ratio of thesecond cross-sectional area C₂ in the discharged state to the firstcross-sectional area C₁ in the charged state. For example, in oneembodiment at least one member of the subset of the population ofcathode structures has a ratio of the second median cross-sectional areaML_(c2) in the discharged state to a first median cross-sectional areaML_(c1) in the charged state that is at least 1.05:1. By way of furtherexample, in one embodiment the at least one member of the subset of thepopulation of cathode structures has a ratio of the second mediancross-sectional area ML_(c2) in the discharged state to a first mediancross-sectional area ML_(c1) in the charged state that is at least1.1:1. By way of further example, in one embodiment the at least onemember of the subset of the population of cathode structures has a ratioof the second median cross-sectional area ML_(c2) in the dischargedstate to a first median cross-sectional area ML_(c1) in the chargedstate that is at least 1.3:1. By way of further example, in oneembodiment the at least one member of the subset of the population ofcathode structures has a ratio of the second median cross-sectional areaML_(c2) in the discharged state to a first median cross-sectional areaML_(c1) in the charged state that is at least 2:1. By way of furtherexample, in one embodiment the at least one member of the subset of thepopulation of cathode structures has a ratio of the second mediancross-sectional area ML_(c2) in the discharged state to a first mediancross-sectional area ML_(c1) in the charged state that is at least 3:1.By way of further example, in one embodiment the at least one member ofthe subset of the population of cathode structures has a ratio of thesecond median cross-sectional area ML_(c2) in the discharged state to afirst median cross-sectional area ML_(c1) in the charged state that isat least 4:1. By way of further example, in one embodiment the at leastone member of the subset of the population of cathode structures has aratio of the second median cross-sectional area ML_(c2) in thedischarged state to a first median cross-sectional area ML_(c1) in thecharged state that is at least 6:1. Generally, the ratio of the secondmedian cross-sectional area ML_(C2) to the first median cross-sectionalarea ML_(C1) will not exceed about 15:1, and even will not exceed 10:1,such as for example may not exceed 8:1. For example, the at least onemember of the subset of the population of cathode structures may have aratio of the second median cross-sectional area ML_(c2) in thedischarged state to a first median cross-sectional area ML_(c1) in thecharged state that may be in the range of from 1.05:1 to 15:1. By way offurther example, the at least one member of the subset of the populationof cathode structures has a ratio of the second median cross-sectionalarea ML_(c2) in the discharged state to a first median cross-sectionalarea ML_(c1) in the charged state that may be in the range of from 1.1:1to 6:1. By way of further example, in one embodiment the at least onemember of the subset of the population of cathode structures has a ratioof the second median cross-sectional area ML_(c2) in the dischargedstate to a first median cross-sectional area ML_(c1) in the chargedstate that may be in the range of from 1.3:1 to 4:1. Furthermore, in oneembodiment, the contraction of the first median cross-sectional areaML_(C1) with respect to the second median cross-sectional area ML_(C2)may be in the range of from 2% contraction to 90% contraction, such asfrom 5% contraction to 75% contraction, and even from 10% contraction to70% contraction. That is, the first median cross-sectional area ML_(C1)may be contracted by at least 2% with respect to the mediancross-sectional area ML_(C2), such as at least 5% and even at least 10%,with respect to ML_(C2), but may be contracted less than 90% withrespect to ML_(C2), such as less than 80% and even less than 75% withrespect to ML_(C2), such as less than 70% with respect to ML_(C2).

Furthermore, in one embodiment, at least one member of the subset of thepopulation of anode structures 110 may have a first mediancross-sectional area ML_(A1) in the charged state that may be the sameas and/or similar to values give above for the first cross-sectionalarea A₁ of a member of the population of anode structures in the chargedstate. For example, in one embodiment, the at least one member of thesubset of the population of anode structures 110 may have a first mediancross-sectional area ML_(A1) in the charged state that is at least 100μm². By way of further example, in one embodiment the at least onemember of the subset of the population of anode structures 110 may havea first median cross-sectional area ML_(A1) in the charged state that isat least 1×10³ μm². By way of yet further example, in one embodiment theat least one member of the subset of the population of anode structures110 may have a first median cross-sectional area ML_(A1) in the chargedstate that is at least 4.7×10³ μm². By way of yet further example, theat least one member of the subset of the population of anode structures110 may have a first median cross-sectional area ML_(A1) in the chargedstate that is at least 6×10³ μm². By way of further example, in oneembodiment the at least one member of the subset of the population ofanode structures 110 may have a first median cross-sectional areaML_(A1) in the charged state that is at least 8×10³ μm². In general, thefirst median cross-sectional area ML_(A1) of the at least one member ofthe subset of the population of anode structures in the charged statemay not exceed 1.5×10⁷ μm², for example the first median cross-sectionalarea ML_(A1) in the charged state of the at least one member may notexceed 6.8×10⁷ μm², and may not even exceed 5×10⁶ μm². For example, thefirst median cross-sectional area ML_(A1) of the at least one member ofthe subset of the population of anode structures may be in the range offrom 100 μm² to 1.5×10⁷ μm², such as from 4.7×10³ μm² to 6.8×10⁶ μm²,and even in the range of from 6×10³ μm² to 5×10⁶ μm².

Furthermore, in one embodiment, at least one member of the subset of thepopulation of anode structures 110 may have a second mediancross-sectional area ML_(A2) in the discharged state that may be thesame as and/or similar to values give above for the firstcross-sectional area A₂ of a member of the population of anodestructures in the charged state. For example, the at least one member ofthe subset of the population of anode structures 110 may have a secondmedian cross-sectional area ML_(A2) in the discharged state that is notmore than 3×10⁷ μm². By way of further example, in one embodiment the atleast one member of the subset of the population of anode structures 110may have a second median cross-sectional area ML_(A2) in the dischargedstate that is not more than 1.5×10⁷ μm². By way of further example, inone embodiment the at least one member of the subset of the populationof anode structures 110 may have a second median cross-sectional areaML_(A2) in the discharged state that is not more than 7.1×10⁶ μm². Byway of further example, in one embodiment the at least one member of thesubset of the population of anode structures 110 may have a secondmedian cross-sectional area ML_(A2) in the discharged state that is notmore than 5×10⁶ μm². By way of further example, in one embodiment the atleast one member of the subset of the population of anode structures 110may have a second median cross-sectional area ML_(A2) in the dischargedstate that is not more than 3×10⁶ μm². In general, the second mediancross-sectional area ML_(A2) of the at least one member of the subset ofthe population of anode structures in the charged state will be at least1.5×10³ μm², for example the second median cross-sectional area ML_(A2)of the at least one member in the discharged state may be at least1.6×10³ μm², and even at least 3×10³ μm². For example, the second mediancross-sectional area ML_(A2) in the discharged state may be in the rangeof from 500 μm² to 3×10⁷ μm², such as from 1.6×10³ μm² to 7.1×10⁶ μm²,and even in the range of from 3×10³ μm² to 5×10⁶ μm².

In yet another embodiment, at least one member of the subset of thepopulation of anode structures 110 may have a ratio of the first mediancross-sectional area ML_(A1) in the charged state to a second mediancross-sectional area ML_(A2) in the discharged state that is the same asand/or similar to the values given above for the ratio of the firstcross-sectional area A₁ in the charged state to the secondcross-sectional area A₂ in the discharged state. For example, in oneembodiment the at least one member of the subset of the population ofanode structures has a ratio of the first median cross-sectional areaML_(A1) in the charged state to a second median cross-sectional areaML_(A2) in the discharged state that is at least 1.01:1. By way offurther example, in one embodiment the at least one member of the subsetof the population of anode structures has a ratio of the first mediancross-sectional area ML_(A1) in the charged state to a second mediancross-sectional area ML_(A2) in the discharged state that is at least1.05:1. By way of further example, in one embodiment the at least onemember of the subset of the population of anode structures has a ratioof the first median cross-sectional area ML_(A1) in the charged state toa second median cross-sectional area ML_(A2) in the discharged statethat is at least 1.5:1. By way of further example, in one embodiment theat least one member of the subset of the population of anode structureshas a ratio of the first median cross-sectional area ML_(A1) in thecharged state to a second median cross-sectional area ML_(A2) in thedischarged state that is at least 2:1. By way of further example, in oneembodiment the at least one member of the subset of the population ofanode structures has a ratio of the first median cross-sectional areaML_(A1) in the charged state to a second median cross-sectional areaML_(A2) in the discharged state that is at least 3:1. By way of furtherexample, in one embodiment the at least one member of the subset of thepopulation of anode structures has a ratio of the first mediancross-sectional area ML_(A1) in the charged state to a second mediancross-sectional area ML_(A2) in the discharged state that is at least4:1. By way of further example, in one embodiment the at least onemember of the subset of the population of anode structures has a ratioof the first median cross-sectional area ML_(A1) in the charged state toa second median cross-sectional area ML_(A2) in the discharged statethat is at least 5:1. For example, in one embodiment the at least onemember of the subset of the population of anode structures has a ratioof the first median cross-sectional area ML_(A1) in the charged state toa second median cross-sectional area ML_(A2) in the discharged statethat may be the range of from 1.01:1 to 5:1. By way of further example,in one embodiment the at least one member of the subset of thepopulation of anode structures has a ratio of the first mediancross-sectional area ML_(A1) in the charged state to a second mediancross-sectional area ML_(A2) in the discharged state that may be in therange of from 1.01:1 to 4:1. By way of further example, in oneembodiment the at least one member of the subset of the population ofanode structures has a ratio of the first median cross-sectional areaML_(A1) in the charged state to a second median cross-sectional areaML_(A2) in the discharged state that may be in the range of from 1.01:1to 3:1, and even in the range of from 1.5:1 to 3:1.

According to yet another embodiment, a median cross-sectional areaMO_(A) and/or MO_(C) can be measured for a subset of the anode structurepopulation and/or cathode structure population, respectively, byevaluating the median of the cross-sectional areas as measured in aplurality of longitudinal planes for each member (e.g., the ML_(A)and/or ML_(C)), and then taking the median of this value as measured fora subset, such as at least two members, of the anode structurepopulation or the anode structure population. That is, the MO_(A) and/orMO_(C) may be understood as an “overall” median of the cross-sectionalareas as measured in a plurality of longitudinal planes, and acrossmultiple anodes and/or cathodes. The subset of the anodes and/orcathodes across which the median is evaluated to obtain the MO_(A)and/or MO_(C) may correspond to any of the subsets described above.Similarly to the MA_(A), ML_(A), MA_(C) and ML_(C) values above, asubset of the population of anode structures has a first mediancross-sectional area MO_(A1) when the secondary battery is in a chargedstate, and a second median cross-sectional area MO_(A2) when thesecondary battery is in the discharged state, and a subset of thepopulation of cathode structures has a first median cross-sectional areaMO_(C1) when the secondary battery is in a charged state, and a secondmedian cross-sectional area MO_(C2) when the secondary battery is in thedischarged state, where MO_(A1) is greater than MO_(A2), and MO_(C1) isless than MO_(C2).

In one embodiment, the subset of the population of cathode structures112 may have a first median cross-sectional area MO_(c1) in the chargedstate that may be the same as and/or similar to values give above forthe first cross-sectional area C₁ of a member of the population ofcathode structures in the charged state. For example, in one embodiment,the subset of the population of cathode structures 112 may have a firstmedian cross-sectional area MO_(C1) in the charged state that is notmore than 3×10⁷ μm². By way of further example, in one embodiment, thesubset of the population of cathode structures 112 may have a firstmedian cross-sectional area MO_(C1) in the charged state that is notmore than 1×10⁷ μm². By way of yet further example, in one embodimentthe subset of the population of cathode structures 112 may have a firstmedian cross-sectional area MO_(C1) in the charged state that is notmore than 9.3×10⁶ μm². By way of yet further example, in one embodiment,the subset of the population of cathode structures 112 may have a firstmedian cross-sectional area MO_(C1) in the charged state that is notmore than 8×10⁶ μm². By way of further example, in one embodiment thesubset of the population of cathode structures 112 may have a firstmedian cross-sectional area MO_(C1) in the charged state that is notmore than 5×10⁶ μm². In general, the first median cross-sectional areaMO_(C1) of the subset of the population of cathode structure may be atleast 2.0×10⁶ μm², for example the first median cross-sectional areaMO_(C1) in the charged state may be at least 2.6×10² μm², and even atleast 5×10² μm². For example, the first median cross-sectional areaMO_(C1) of the subset of the population of cathode structures may be inthe range of from 1×10² μm² to 3×10⁷ μm², such as from 2.6×10² μm² to9.03×10⁶ μm², and even in the range of from 3×10² μm² to 8×10⁶ μm².

Furthermore, in one embodiment, the subset of the population of cathodestructures 112 may have a second median cross-sectional area MO_(c2) inthe discharged state that may be the same as and/or similar to valuesgive above for the second cross-sectional area C₂ of a member of thepopulation of cathode structures in the discharged state. For example,in one embodiment, the subset of the population of cathode structures112 may have a second median cross-sectional area MO_(C2) in the chargedstate in the discharged state that is at least 1.01×10² μm². By way offurther example, in one embodiment the subset of the population ofcathode structures 112 may have a second median cross-sectional areaMO_(C2) in the discharged state that is at least 1.05×10² μm². By way offurther example, in one embodiment the subset of the population ofcathode structures 112 may have a second median cross-sectional areaMO_(C2) in the discharged state that is at least 1.05×10³ μm². By way offurther example, the subset of the population of cathode structures 112may have a second median cross-sectional area MO_(C2) in the dischargedstate that is at least 1.1×10³ μm². By way of further example, in oneembodiment the subset of the population of cathode structures 112 mayhave a second median cross-sectional area MO_(C2) in the dischargedstate that is at least 1.5×10³ μm². In general, the second mediancross-sectional area MO_(c2) of the subset of the population of cathodestructures in the discharged state will not exceed 1.5×10¹⁰ μm², forexample the second median cross-sectional area MO_(c2) in the dischargedstate may not exceed 9.5×10⁶ μm², and may even not exceed 1×10⁶ μm². Forexample, the second median cross-sectional area MO_(C2) of the subset ofthe population of cathode structures in the discharged state may be inthe range of from 1.01×10² μm² to 1.5×10¹⁰ μm², such as from 1.05×10³μm² to 9.5×10⁶ μm², and even in the range of from 1.1×10² μm² to 1×10⁶μm².

In yet another embodiment, in one embodiment the subset of thepopulation of cathode structures 112 may have a ratio of the secondmedian cross-sectional area MO_(c2) in the discharged state to a firstmedian cross-sectional area MOC1 in the charged state that may be thesame as and/or similar to values give above for the ratio of the secondcross-sectional area C₂ of a member of the population of cathodestructures in the discharged state to the first cross-sectional area C1of the member of the population of cathode structures in the chargedstate. For example, in one embodiment, the subset of the population ofcathode structures has a ratio of the second median cross-sectional areaMO_(c2) in the discharged state to a first median cross-sectional areaMO_(c1) in the charged state that is at least 1.05:1. By way of furtherexample, in one embodiment the subset of the population of cathodestructures has a ratio of the second median cross-sectional area MO_(c2)in the discharged state to a first median cross-sectional area MO_(c1)in the charged state that is at least 1.1:1. By way of further example,in one embodiment the subset of the population of cathode structures hasa ratio of the second median cross-sectional area MO_(c2) in thedischarged state to a first median cross-sectional area MO_(c1) in thecharged state that is at least 1.3:1. By way of further example, in oneembodiment the subset of the population of cathode structures has aratio of the second median cross-sectional area MO_(c2) in thedischarged state to a first median cross-sectional area MO_(c1) in thecharged state that is at least 2:1. By way of further example, in oneembodiment the subset of the population of cathode structures has aratio of the second median cross-sectional area MO_(c2) in thedischarged state to a first median cross-sectional area MO_(c1) in thecharged state that is at least 3:1. By way of further example, in oneembodiment the subset of the population of cathode structures has aratio of the second median cross-sectional area MO_(c2) in thedischarged state to a first median cross-sectional area MO_(c1) in thecharged state that is at least 4:1. By way of further example, in oneembodiment the subset of the population of cathode structures has aratio of the second median cross-sectional area MO_(c2) in thedischarged state to a first median cross-sectional area MO_(c1) in thecharged state that is at least 6:1. Generally, the ratio of the secondmedian cross-sectional area MO_(C2) to the first median cross-sectionalarea MO_(C1) will not exceed about 15:1, and will not even exceed 10:1,and may not exceed for example 8:1. For example, the subset of thepopulation of cathode structures has a ratio of the second mediancross-sectional area MO_(c2) in the discharged state to a first mediancross-sectional area MO_(c1) in the charged state that may be in therange of from 1.05:1 to 6:1. By way of further example, the subset ofthe population of cathode structures has a ratio of the second mediancross-sectional area MO_(c2) in the discharged state to a first mediancross-sectional area MO_(c1) in the charged state that may be in therange of from 1.1:1 to 4:1. By way of further example, the subset of thepopulation of cathode structures has a ratio of the second mediancross-sectional area MO_(c2) in the discharged state to a first mediancross-sectional area MO_(c1) in the charged state that may be in therange of from 1.3:1 to 4:1. Furthermore, in one embodiment, thecontraction of the first median cross-sectional area MO_(C1) withrespect to the second median cross-sectional area MO_(C2) may be in therange of from 2% contraction to 90% contraction, such as from 5%contraction to 75% contraction, and even from 10% contraction to 70%contraction. That is, the first median cross-sectional area MO_(C1) maybe contracted by at least 2% with respect to the median cross-sectionalarea MO_(C2), such as at least 5% and even at least 10%, with respect toMO_(C2), but may be contracted less than 90% with respect to MO_(C2),such as less than 80% and even less than 75% with respect to MO_(C2),such as less than 70% with respect to MO_(C2).

Furthermore, in one embodiment, the subset of the population of anodestructures 110 may have a first median cross-sectional area MO_(A1) inthe charged state that may be the same as and/or similar to values giveabove for the first cross-sectional area A₁ of a member of thepopulation of anode structures in the charged state. For example, in oneembodiment, the subset of the population of anode structures 110 mayhave a first median cross-sectional area MO_(A1) in the charged statethat is greater than 100. By way of further example, in one embodimentthe subset of the population of anode structures 110 may have a firstmedian cross-sectional area MO_(A1) in the charged state that is atleast 100 μm². By way of yet further example, in one embodiment thesubset of the population of anode structures 110 may have a first mediancross-sectional area MO_(A1) in the charged state that is at least 1×10³μm². By way of yet further example, the subset of the population ofanode structures 110 may have a first median cross-sectional areaMO_(A1) in the charged state that is at least 4.7×10³ μm². By way offurther example, in one embodiment the subset of the population of anodestructures 110 may have a first median cross-sectional area MO_(A1) inthe charged state that is at least 6×10³ μm². By way of further example,in one embodiment the subset of the population of anode structures 110may have a first median cross-sectional area MO_(A1) in the chargedstate that is at least 8×10³ μm². In general, the first mediancross-sectional area MO_(A1) of the subset of the population of anodestructures in the charged state may not exceed 1.5×10⁷ μm², for examplethe first median cross-sectional area MO_(A1) in the charged state maynot exceed 6.8×10⁷ μm², and may even not exceed 5×10⁶ μm². For example,the first median cross-sectional area MO_(A1) in the charged state maybe in the range of from 100 μm² to 1.5×10⁷ μm², such as from 4.7×10³ μm²to 6.8×10⁶ μm², and may even be in the range of from 6×10³ μm² to 5×10⁶μm².

Furthermore, in one embodiment, the subset of the population of anodestructures 110 may have a second median cross-sectional area MO_(A2) inthe discharged state that may be the same as and/or similar to valuesgive above for the second cross-sectional area A2 of a member of thepopulation of anode structures in the discharged state. For example, inone embodiment, the subset of the population of anode structures 110 mayhave a second median cross-sectional area MO_(A2) in the dischargedstate that is no more than 3.3×10⁷ μm². By way of further example, inone embodiment the subset of the population of anode structures 110 mayhave a second median cross-sectional area MO_(A2) in the dischargedstate that is no more than 1.5×10⁷ μm². By way of further example, inone embodiment the subset of the population of anode structures 110 mayhave a second median cross-sectional area MO_(A2) in the dischargedstate that is no more than 7.1×10⁶ μm². By way of further example, inone embodiment the subset of the population of anode structures 110 mayhave a second median cross-sectional area MO_(A2) in the dischargedstate that is no more than 5×10⁶ μm². By way of further example, in oneembodiment the subset of the population of anode structures 110 may havea second median cross-sectional area MO_(A2) in the discharged statethat is no more than 3×10⁶ μm². In general, the second mediancross-sectional area MO_(A2) of the subset of the population of anodestructures in the charged state will be at least 1.5×10³ μm², forexample the second median cross-sectional area MO_(A2) in the dischargedstate may be at least 1.6×10³ μm², and even at least 3×10³ μm². Forexample, the second median cross-sectional area MO_(A2) of the subset ofthe population of anode structures in the charged state may be in therange of from 500 μm² to 3×10⁷ μm², such as from 1.6×10³ μm² to 7.1×10⁶μm², and even in the range of from 3×10³ μm² to 5×10⁶ μm².

In yet another embodiment, the subset of the population of anodestructures 110 may have a ratio of the first median cross-sectional areaMO_(A1) in the charged state to a second median cross-sectional areaMO_(A2) in the discharged state that may be the same as and/or similarto values give above for the ratio of the first cross-sectional area A₁of a member of the population of anode structures in the charged stateto the second cross-sectional area A₂ of the member of the population ofanode structures in the discharged state. For example, in one embodimentthe subset of the population of anode structures has a ratio of thefirst median cross-sectional area MO_(A1) in the charged state to asecond median cross-sectional area MO_(A2) in the discharged state thatis at least 1.01:1. By way of further example, in one embodiment thesubset of the population of anode structures has a ratio of the firstmedian cross-sectional area MO_(A1) in the charged state to a secondmedian cross-sectional area MO_(A2) in the discharged state that is atleast 1.05:1. By way of further example, in one embodiment the subset ofthe population of anode structures has a ratio of the first mediancross-sectional area MO_(A1) in the charged state to a second mediancross-sectional area MO_(A2) in the discharged state that is at least1.5:1. By way of further example, in one embodiment the subset of thepopulation of anode structures has a ratio of the first mediancross-sectional area MO_(A1) in the charged state to a second mediancross-sectional area MO_(A2) in the discharged state that is at least2:1. By way of further example, in one embodiment the subset of thepopulation of anode structures has a ratio of the first mediancross-sectional area MO_(A1) in the charged state to a second mediancross-sectional area MO_(A2) in the discharged state that is at least3:1. By way of further example, in one embodiment the subset of thepopulation of anode structures has a ratio of the first mediancross-sectional area MO_(A1) in the charged state to a second mediancross-sectional area MO_(A2) in the discharged state that is at least4:1. By way of further example, in one embodiment the subset of thepopulation of anode structures has a ratio of the first mediancross-sectional area MO_(A1) in the charged state to a second mediancross-sectional area MO_(A2) in the discharged state that is at least5:1. For example, in one embodiment the subset of the population ofanode structures has a ratio of the first median cross-sectional areaMO_(A1) in the charged state to a second median cross-sectional areaMO_(A2) in the discharged state that may be the range of from 1.01 to4:1. By way of further example, in one embodiment the subset of thepopulation of anode structures has a ratio of the first mediancross-sectional area MO_(A1) in the charged state to a second mediancross-sectional area MO_(A2) in the discharged state that may be in therange of from 1.01:1 to 3:1, and even in the range of from 1.5:1 to 3:1.

In yet another embodiment, the change in size of the member of the anodeand/or cathode structure population that can occur upon charging and/ordischarging of the secondary battery is reflected in the change in widthof a subset of one or more of the anode and cathode structurepopulation. As has also similarly been discussed above, a subset of thepopulation of anode structures may have a first width W_(A1) when thesecondary battery is in the charged state, and a second width W_(A2)when the secondary battery is in the discharged state, and a subset ofthe population of cathode structures may have a first width W_(C1) whenthe secondary battery is in the charged state, and a second width W_(C2)when the secondary battery is in the discharged state, where W_(A1) isgreater than W_(A2) and W_(C1) is less than W_(C2). In one embodiment,the widths W_(A) and W_(C) are measured by measuring the distancebetween points on a line that is formed by bisection of the firstlongitudinal plane 113 with an orthogonal X-Y plane 123, where theY-axis is parallel to the longitudinal direction, and the X-axis isparallel to a direction of the lengths L_(A) and LC of the member of theanode and cathode structure populations, respectively. For example,referring to FIG. 1D, the widths may be measured along the line thatforms from the bisection of the longitudinal plane 113 with an X-Y plane123, from a first point 125 a on the first side of the member, to asecond point 125 b on the same line on the second side of the member. Inone embodiment, the X-Y plane 123 may be located at a midpoint of theheight H_(A) or H_(C) of one or more of the members of the anode and/orcathode structure populations, where the height is measured in adirection orthogonal to both the longitudinal direction and thedirection of the lengths L_(A) and L_(C) of the members of the anodeand/or cathode structure populations. In another embodiment, the X-Yplane is located at a position along the height of the electrodes (e.g.,H_(A) and/or H_(C)) that is anywhere from 25% to 75% of the total heightH of members of the cathode and/or anode structure populations.Alternatively and/or additionally, the width of the member of the anodestructure and/or cathode structure population may correspond to theFeret diameter of the member as measured in the width direction (e.g.,along the longitudinal axis) of the member, where the Feret diameter isthe distance between two parallel planes restricting the member in thewidth direction, as measured in a direction parallel to the two planes.

Accordingly, in one embodiment, a subset of the population of cathodestructures 112 have a first width W_(C1) in the charged state that is nomore than 5000 μm. By way of further example, in one embodiment a subsetof the members of the population of cathode structures have a firstwidth W_(C1) in the charged state that is no more than 3000 μm. By wayof yet further example, in one embodiment a subset of the members of thepopulation of cathode structures have a first width W_(C1) in thecharged state that is less than 1.9×10³ μm. By way of yet furtherexample, in one embodiment a subset of the members of the population ofcathode structures have a first width W_(C1) in the charged state thatis no more than 1000 μm. By way of further example, in one embodiment asubset of the members of the population of cathode structures have afirst width W_(C1) in the charged state that is no more than 500 μm.Generally, the first width WC1 in the charged state will be at least 2μm, such as at least 5 μm, and even at least 15 μm. For example, in oneembodiment, a subset of members of the population of cathode structuresmay have a first width W_(C1) in the charged state that may be in therange of from 2 μm to 5000 μm, such as from 5 μm to 1900 μm, and evenfrom 15 μm to 1000 μm.

In one embodiment, a subset of the members of the population of cathodestructures have a second width W_(C2) in the discharged state that is atleast 5 μm. By way of further example, in one embodiment a subset of themembers of the population of cathode structures have a second widthW_(C2) in the discharged state that is at least 10 μm. By way of furtherexample, in one embodiment a subset of the members of the population ofcathode structures have a second width W_(C2) in the discharged statethat is at least 20 μm. By way of further example, in one embodiment asubset of the members of the population of cathode structures have asecond width W_(C2) in the discharged state that is at least 50 μm. Byway of further example, in one embodiment a subset of the members of thepopulation of cathode structures have a second width W_(C2) in thedischarged state that is at least 100 μm. Generally, the second widthW_(C2) in the discharged state will be less than 5,000 μm, such as lessthan 2,000 μm and even less than 1000 μm. For example, in oneembodiment, a subset of members of the population of cathode structures112 have a second width W_(C2) in the discharged state that is in therange of from 5 μm to 5,000 μm, such as from 20 μm to 2,000 μm, and evenfrom 50 μm to 1000 μm.

In yet another embodiment, in one embodiment a ratio of the second widthW_(C2) of the cathode structure 112 in the discharged state to a firstwidth W_(C1) of the cathode structure 112 in the charged state for asubset of the population is at least 1.05:1. By way of further example,in one embodiment a ratio of the second width W_(C2) of the cathodestructure 112 to the first width W_(C1) of the cathode structure 112 fora subset of the population is at least 1.1:1. By way of further example,in one embodiment a ratio of the second width W_(C2) of the cathodestructure 112 to the first width W_(C2) of the cathode structure 112 fora subset of the population is at least 1.3:1. By way of further example,in one embodiment a ratio of the second width W_(C2) of the cathodestructure 112 to the first width W_(C2) of the cathode structure 112 fora subset of the population is at least 2:1. By way of further example,in one embodiment a ratio of the second width W_(C2) of the cathodestructure 112 to the first width W_(C1) of the cathode structure 112 fora subset of the population is at least 3:1. By way of further example,in one embodiment a ratio of the second width W_(C2) of the cathodestructure 112 to the first width W_(C1) of the cathode structure 112 fora subset of the population is at least 4:1. By way of further example,in one embodiment a ratio of the second width W_(C2) of the cathodestructure 112 to the first width W_(C1) of the cathode structure 112 fora subset of the population is at least 6:1. Generally a ratio of thesecond width W_(C2) to the first width W_(C1) will not exceed 15:1, suchas not exceeding 10:1, and even not exceeding 8:1. For example, in oneembodiment a ratio of the second width W_(C2) of the cathode structure112 to the first width W_(C1) of the cathode structure 112 for a subsetof the population may be in the range of from 1.05:1 to 15:1. By way offurther example, in one embodiment a ratio of the second width W_(C2) ofthe cathode structure 112 to the first width W_(C1) of the cathodestructure 112 for a subset of the population may be in the range of from1.1:1 to 6:1. By way of further example, in one embodiment a ratio ofthe second width W_(C2) of the cathode structure 112 to the first widthW_(C1) of the cathode structure 112 for a subset of the population maybe in the range of from 1.3:1 to 4:1. By way of further example, in oneembodiment the contraction of the first width W_(C1) with respect to thesecond width W_(C2) may be in the range of from 2% contraction to 90%contraction, such as from 5% contraction to 75% contraction. That is,the first width W_(C1) may be contracted by at least 2% with respect tothe second median width W_(C2), such as at least 5% and even at least10% with respect to the second width W_(C2), but may be contracted lessthan 90% with respect to the second width W_(C2), such as less than 80%and even less than 75% with respect to the second width W_(C2).

Furthermore, in one embodiment, a subset of the population of anodestructures 110 may have a first width W_(A1) in the charged state thatis at least 50 μm. By way of further example, in one embodiment a subsetof the members of the population of anode structures have a first widthW_(A1) in the charged state that is at least 75 μm. By way of yetfurther example, in one embodiment a subset of the members of thepopulation of anode structures have a first width W_(A1) in the chargedstate that is at least 90 μm. By way of yet further example, in oneembodiment a subset of the members of the population of anode structureshave a first width W_(A1) in the charged state that is at least 150 μm.By way of further example, in one embodiment a subset of the members ofthe population of anode structures have a first width W_(A1) in thecharged state that is at least 200 μm. Generally, the first width W_(A1)in the charged state will not exceed 2000 μm, such as not exceeding 1520μm and even not exceeding 1000 μm. For example, in one embodiment, asubset of members of the population of anode structures 110 have a firstwidth W_(A1) in the charged state that is in the range of from 50 μm to2000 μm, such as from 90 μm to 1520 μm, and even from 150 μm to 1000 μm.

In one embodiment, a subset of the members of the population of anodestructures have a second width W_(A2) in the discharged state that is nomore than 2500 μm. By way of further example, in one embodiment a subsetof the members of the population of anode structures have a second widthW_(A2) in the discharged state that is no more than 2000 μm. By way offurther example, in one embodiment a subset of the members of thepopulation of anode structures have a second width W_(A2) in thedischarged state that is no more than 1500 μm. By way of furtherexample, in one embodiment a subset of the members of the population ofanode structures have a second width W_(A2) in the discharged state thatis no more than 1000 μm. By way of further example, in one embodiment asubset of the members of the population of anode structures have asecond width W_(A2) in the discharged state that is no more than 800 μm.Generally, the second width W_(A2) in the discharged state will be atleast 15 μm, such as at least 30 μm, and even at least 60 μm. Forexample, in one embodiment, a subset of members of the population ofanode structures 110 have a second width W_(A2) in the discharged statethat is in the range of from 15 μm to 2500 μm, such as from 30 μm to1500 μm, and even from 60 μm to 1000 μm.

In yet another embodiment, a ratio of the first width W_(A1) of theanode structure 110 in the charged state to a second width W_(A2) of theanode structure 110 in the discharged state for a subset of thepopulation is at least 1.01:1. By way of further example, in oneembodiment a ratio of the first width W_(A1) of the anode structure 110in the charged state to a second width W_(A2) of the anode structure 110in the discharged state for a subset of the population is at least1.05:1. By way of further example, in one embodiment a ratio of thefirst width W_(A1) of the anode structure 110 in the charged state to asecond width W_(A2) of the anode structure 110 in the discharged statefor a subset of the population is at least 1.5:1. By way of furtherexample, in one embodiment a ratio of the first width W_(A1) of theanode structure 110 in the charged state to a second width W_(A2) of theanode structure 110 in the discharged state for a subset of thepopulation is at least 2:1. By way of further example, in one embodimenta ratio of the first width W_(A1) of the anode structure 110 in thecharged state to a second width W_(A2) of the anode structure 110 in thedischarged state for a subset of the population is at least 3:1. By wayof further example, in one embodiment a ratio of the first width W_(A1)of the anode structure 110 in the charged state to a second width W_(A2)of the anode structure 110 in the discharged state for a subset of thepopulation is at least 4:1. By way of further example, in one embodimenta ratio of the first width W_(A1) of the anode structure 110 in thecharged state to a second width W_(A2) of the anode structure 110 in thedischarged state for a subset of the population is at least 5:1. Forexample, in one embodiment a ratio of the first width W_(A1) of theanode structure 110 in the charged state to a second width W_(A2) of theanode structure 110 in the discharged state for a subset of thepopulation may be in the range of from 1.0:1 to 5:1. By way of furtherexample, in one embodiment a ratio of the first width W_(A1) of theanode structure 110 in the charged state to a second width W_(A2) of theanode structure 110 in the discharged state for a subset of thepopulation may be in the range of from 1.01:1 to 4:1. By way of furtherexample, in one embodiment a ratio of the first width W_(A1) of theanode structure 110 in the charged state to a second width W_(A2) of theanode structure 110 in the discharged state for a subset of thepopulation may be may be in the range of from 1.01:1 to 3:1, and mayeven be in the range of from 1.5:1 to 3:1.

In one embodiment, the sizes (e.g. dimensions and cross-sectional areas)for the members of the population of anode structures 110 and cathodestructures 112 in the charged and discharged states, such as thosedescribed above, are those achieved in charging and/or discharging stepsthat are performed after an initial formation stage for the secondarybattery 102 has already been performed. That is, in the manufacture of asecondary battery 102 having the electrode assembly 106, an initialformation stage may be performed that comprises at least one initialcharging cycle of the secondary battery 102, which may be performedunder carefully controlled conditions including one or more of current,temperature and duration, to promote the formation of the desiredstructure and contact between components of the secondary battery 102.The initial formation stage can comprise only a single initial chargingcycle, or may comprise a plurality of charging cycles, according to theparticular battery structure and composition, and which can be performedas a final stage in manufacturing to bring the secondary battery 102 toits full power and/or capacity. According to one embodiment, one or moredimensions of the anode and/or cathode structures may also change duringthe initial formation stage, as the secondary battery 102 is chargedand/or discharged, as is also discussed in further detail below.Accordingly, in one embodiment, the dimensions of the cathode and anodestructures 110, 112 referred to herein, as well as the changes therein,are those that occur during charging and/or discharging of the secondarybattery subsequent to the initial formation stage. However, in anotherembodiment, the dimensions referred to herein, as well as the changestherein, may also correspond to those that occur as a part of theinitial formation stage.

In one embodiment, members of the population of cathode structures 110comprise a cathode active material layer 138 having a porous structure,where the porosity of the cathode active material layer 138 may changeaccording to the expansion/contraction of the cathode structures 112upon charging/discharging of the secondary battery 102. For example,referring to FIG. 3, members of the population of cathode structures 112may comprise a cathode active material layer 138 having cathode activematerial 202 distributed in a porous matrix 204 of material, with theporous matrix 204 comprising pores 200 and/or interstices formedtherein. In the embodiment as shown in FIG. 3, the cathode activematerial layer 138 comprises particles 202 of cathode active materialthat are dispersed in the porous matrix 204. The cathode active materiallayer 138 may also optionally comprise filler particles 206 that aresimilarly dispersed in the porous matrix 204. In the embodiment asshown, the porous matrix is relatively highly porous, and comprises websand/or strands of matrix material connecting the particles 202 ofcathode active material and/or particles 206 of filler material, withpores 200 and/or interstices formed between adjacent webs and/or strandsof matrix material. The porous matrix 204 may thus be understood, in oneembodiment, to act as a binder that binds the particles of cathodeactive material together to form the cathode active material layer 138.In another embodiment, the porous matrix 204 can also and/oralternatively comprise thicker sections of matrix material having theparticles 202 at least partially and even entirely embedded therein,with pores formed in the relatively thick matrix material sections. Incertain embodiments the porosity (i.e. void fraction) of the matrix 204,which may be related to the volume and/or number of pores 202 and/orinterstices in the matrix material, and which can vary according to thecharge/discharge state of the secondary battery 102, can also beselected to provide performance of the cathode active material layer138, as is discussed in more detail below.

According to one embodiment, compression and/or expansion of members ofthe population of cathode structures 112 may result in compressionand/or expansion of the cathode active material layer 138, such that thepores and/or interstices 200 increase in size and/or number uponexpansion of members of the population of cathode structures 112, anddecrease in size and/or number upon compression of members of thepopulation of cathode structures 112. That is, the compression and/orexpansion of the members of the population of cathode structures 112during cycling of the secondary battery 102 between charged anddischarged states results in a change in porosity of the cathode activematerial layer 138. In the embodiment shown in FIGS. 4A-4B, the membersof the population of cathode structures 112 are depicted as being in acharged state with a width W_(C1) in FIG. 4A, and a discharged statewith a width W_(C2) in FIG. 4B, where the width W_(C2) is greater thanthe width W_(C1). Similarly, the cross-sectional area C₂ of the membersof the population of cathode structures 112 are higher in the dischargedstate depicted in FIG. 4B than the cross-sectional area C₁ in thecharged state depicted in FIG. 4A. That is, the members of thepopulation of cathode structures 112 are depicted as being in a morecompressed state in FIG. 4A, and a more expanded state in FIG. 4B,corresponding to, e.g., a charged state and discharged state of thesecondary battery 102, respectively. It is noted that FIGS. 4A-4Bfurther depict an anode structure 110 having an anode active materiallayer 132, anode current collector 136, and anode backbone 134,separators 130 between the anode structure population members 110 andcathode structure population members 112, and cathode structures 112having a cathode backbone 141 and cathode current collectors 140.However, it should be understood that the electrode assembly 106 havingthe anode and cathode structures 110, 112 is not limited thereto, andother structures and/or arrangements of components of the anode andcathode structures can also be provided. As can be seen by theembodiments shown in FIGS. 4A-4B, the expansion of the members of thepopulation of cathode structures 112 from the charged state as depictedin FIG. 4A to the discharged state as depicted in FIG. 4B can result inan increase in the size and/or number of the pores and/or interstices200, as the cathode active material layer 138 expands according to theincreased volume of the discharged state. Conversely, the contraction ofmembers of the population of the cathode structures 112 from thedischarged state as depicted in FIG. 4B to the charged state as depictedin FIG. 4A, results in compression of the cathode active material layer138 and at least partial filling of the pores and/or interstices, as thecathode active material layer 138 is compressed down to the smallervolume of the charged state.

Accordingly, in one embodiment, members of the population of cathodestructures 112 have a cathode active material layer 138 with a firstporosity P₁ when the secondary battery 102 is in the charged state, anda second porosity P₂ when the secondary battery 102 in the dischargedstate, with the first porosity being less than the second porosity. Forexample, in one embodiment, the first porosity may be less than 30%. Byway of further example, in one embodiment, the first porosity may beless than 20%. By way of further example, in one embodiment, the firstporosity may be less than 10%. By way of further example, in oneembodiment, the first porosity may be less than 5%. For example, in oneembodiment, the first porosity may be in the range of from 1 to 30%. Byway of further example, in one embodiment, the first porosity may be inthe range of from 2% to 20%. By way of further example, in oneembodiment, the first porosity may be in the range of from 5% to 10%.Furthermore, in one embodiment, the second porosity in the dischargedmay be at least 50%. For example, in one embodiment, the second porositymay be at least 60%. By way of further example, in one embodiment, thesecond porosity may be at least 70%. By way of further example, in oneembodiment the second porosity may be at least 75%. For example, in oneembodiment, the second porosity may be in the range of from 50% to 90%.By way of further example, in one embodiment, the second porosity may bein the range of from 60% to 80%. By way of further example, in oneembodiment, the second porosity may be in the range of from 70% to 75%.The porosity of the cathode active material layer 138 is the ratio ofthe volume of pores and/or interstices 200 in between cathode activematerial 202 in the cathode active material layer 138, to the volumetaken up by the entire mass of the cathode active material layer 138.

In yet another embodiment, a ratio of the porosity P₂ of the cathodeactive material layer 138 in the discharged state to the porosity P₁ ofthe cathode active material layer 138 in the charged state is at least1.1:1. By way of further example, in one embodiment, a ratio of theporosity P₂ of the cathode active material layer 138 in the dischargedstate to the porosity P₁ of the cathode active material layer 138 in thecharged state is at least 1.5:1. By way of further example, in oneembodiment, a ratio of the porosity P₂ of the cathode active materiallayer 138 in the discharged state to the porosity P₁ of the cathodeactive material layer 138 in the charged state is at least 2:1. By wayof further example, in one embodiment, a ratio of the porosity P₂ of thecathode active material layer 138 in the discharged state to theporosity P₁ of the cathode active material layer 138 in the chargedstate is at least 5:1. By way of further example, in one embodiment, aratio of the porosity P₂ of the cathode active material layer 138 in thedischarged state to the porosity P₁ of the cathode active material layer138 in the charged state is at least 10:1. By way of further example, inone embodiment, a ratio of the porosity P₂ of the cathode activematerial layer 138 in the discharged state to the porosity P₁ of thecathode active material layer 138 in the charged state is at least 15:1.For example, in one embodiment, a ratio of the porosity P₂ of thecathode active material layer 138 in the discharged state to theporosity P₁ of the cathode active material layer 138 in the chargedstate is in the range of from 2:1 to 30:1. For example, in oneembodiment, a ratio of the porosity P₂ of the cathode active materiallayer 138 in the discharged state to the porosity P₁ of the cathodeactive material layer 138 in the charged state is in the range of from3:1 to 20:1. By way of further example, in one embodiment, a ratio ofthe porosity P₂ of the cathode active material layer 138 in thedischarged state to the porosity P₁ of the cathode active material layer138 in the charged state is in the range of from 5:1 to 15:1.

In one embodiment, the cathode active material layer 138 comprisescathode active material in the form of particles 202. For example, inone embodiment, the cathode active material comprises particles 202 ofat least one of transition metal oxides, transition metal sulfides,transition metal nitrides, lithium-transition metal oxides,lithium-transition metal sulfides, and lithium-transition metal nitridesmay be selectively used. The transition metal elements of thesetransition metal oxides, transition metal sulfides, and transition metalnitrides can include metal elements having a d-shell or f-shell.Specific examples of such metal element are Sc, Y, lanthanoids,actinoids, Ti, Zr, Hf, V, Nb, Ta, Cr, Mo, W, Mn, Tc, Re, Fe, Ru, Os, Co,Rh, Ir, Ni, Pb, Pt, Cu, Ag, and Au. Additional cathode active materialsinclude LiCoO₂, LiNi_(0.5)Mn_(1.5)O₄, Li(Ni_(x)Co_(y)Al₂)O₂, LiFePO₄,Li₂MnO₄, V₂O₅, molybdenum oxysulfides, phosphates, silicates, vanadatesand combinations thereof. In one embodiment, the cathode active materiallayer 138 comprises at least 40% by weight of cathode active material202. For example, in one embodiment, the cathode active material layer138 comprises at least 50% by weight of cathode active material. By wayof further example, in one embodiment, the cathode active material layer138 comprises at least 60% by weight of cathode active material. Forexample, the cathode active material layer 138 may comprise a weightpercent of cathode active material in the range of from 40% to 99%. Forexample, in one embodiment, a weight percent of cathode active materialin the cathode active material layer 138 may be in the range of from 50%to 99%. Furthermore, in one embodiment, the cathode active materiallayer 138 comprises at least one filler material, which may also be inthe form of particles. For example, the cathode active material layer138 may comprise filler particles comprising at least one ofcarbon-containing material such as carbon black, polymer-containingbeads such as beads formed from one or more of polyethylene,polypropylene, polyvinylidene fluoride, polytetrafluoroethylene,polyacrylic acid, carboxymethyl cellulose, polyvinylalcohol, starch,regenerated cellulose, diacetyl cellulose, hydroxypropyl cellulose,polyvinyl chloride, polyvinyl pyrrolidone, polybutadiene, polyethyleneoxide, polyacrylates, rubbers, e.g. ethylene-propylene-diene monomer(EPDM) rubber, sulfonated EPDM, fluorinated rubbers, styrene butadienerubber (SBR), polyacrylonitrile (PAN), polymethyl methacrylate (PMMA),polyacrylic acid (PAA), cross-linked polyethylene (PEX, XLPE),polyethylene (PE), polyethylene terephthalate (PET), polyphenyl ether(PPE), polyvinyl chloride (PVC), polyvinylidene chloride (PVDC),polyamide (PA), polyimide (PI), polycarbonate (PC),polytetrafluoroethylene (PTFE), polystyrene (PS), polyurethane (PU),polyester (PE), acrylonitrile butadiene styrene (ABS), polyoxymethylene(POM), polysulfone (PES), styrene-acrylonitrile (SAN), ethylene vinylacetate (EVA), styrene maleic anhydride (SMA), combinations of these,and other inert polymers that have elastic modulus between 1 E-5 GPa and10 GPa), and are inert in the battery. In particular, concentrations andparticle sizes of these materials can be chosen by engineering design ofproperties in order to achieve a predeterrnined compressibility of thecathode structure. For example, in one embodiment, to obtain a cathodestructure with a cathode active material layer having a relatively highcompressibility, polymers with a relatively low elastic modulus (Young'sModulus) can be provided in relatively high concentrations in thecathode active material layer. The particles of filler and/or cathodeactive material may be dispersed in the matrix material, as shown forexample in FIG. 3.

In one embodiment, the cathode active material 202 comprises particles(e.g., one or more of cathode active material particles and fillerparticles) having an average particle size in the range of from 0.1 μmto 500 μm. By way of further example, in one embodiment, the cathodeactive material 202 comprises particles having a weight average particlesize in the range of from 0.15 μm to 300 μm. By way of further example,in one embodiment, the cathode active material 202 comprises particleshaving an average particle size in the range of from 0.2 μm to 200 μm.

In one embodiment, the cathode active material layer 138 comprisesfiller material in a range of from 0.05% by weight to 20% by weight ofthe cathode active material layer. By way of further example, in oneembodiment, the cathode active material layer 138 comprises fillermaterial in a range of from 0.1%. A by weight to 10% by weight. By wayof further example, in one embodiment, the cathode active material layer138 comprises filler material in a range of from 0.5% by weight to 5% byweight.

In yet another embodiment, a ratio by weight of cathode active materialto filler material in the cathode active material layer 138 is in arange of from 1.5:1 to 30:1. In yet another embodiment, a ratio byweight of cathode active material to filler in the cathode activematerial layer 138 is in a range of from 2:1 to 20:1. In yet anotherembodiment, a ratio by weight of cathode active material to filler inthe cathode active material layer 138 is in a range of from 3:1 to 15:1.

According to one embodiment, the cathode active material layer 138comprises particles of cathode active material and/or filler particlesthat are dispersed in the matrix of polymeric material. In oneembodiment, the particles of cathode active material may be dispersedsubstantially uniformly throughout the matrix of polymeric material.Alternatively, in another embodiment, the particles of cathode activematerial may be distributed non-uniformly throughout the matrix ofpolymeric material, such as to provide a gradient of the cathode activematerial throughout the cathode active material layer 138, with a higherconcentration of particles on one side of the cathode active materiallayer 138 than on another side of the cathode active material layer. Inone embodiment, the polymeric material may comprise a fluoropolymerderived from monomers comprising at least one of vinylidene fluoride,hexafluoropropylene, tetrafluoropropene, and the like. In anotherembodiment, the polymeric material may be a polyolefin such as at leastone of polyethylene, polypropylene, or polybutene, having any of a rangeof varying molecular weights and densities. In another embodiment, thepolymeric material is selected from the group consisting ofethylene-diene-propene terpolymer, polystyrene, polymethyl methacrylate,polyethylene glycol, polyvinyl acetate, polyvinyl butyral, polyacetal,and polyethyleneglycol diacrylate. In another embodiment, the polymericmaterial is selected from the group consisting of methyl cellulose,carboxymethyl cellulose, styrene rubber, butadiene rubber,styrene-butadiene rubber, isoprene rubber, polyacrylamide, polyvinylether, polyacrylic acid, polymethacrylic acid, and polyethylene oxide.In another embodiment, the polymeric material is selected from the groupconsisting of acrylates, styrenes, epoxies, and silicones. In yetanother embodiment, the polymeric material can comprise one or more ofpolyethylene, polypropylene, polyvinylidene fluoride,polytetrafluoroethylene, polyacrylic acid, carboxymethyl cellulose,polyvinylalcohol, starch, regenerated cellulose, diacetyl cellulose,hydroxypropyl cellulose, polyvinyl chloride, polyvinyl pyrrolidone,polybutadiene, polyethylene oxide, polyacrylates, rubbers, e.g.ethylene-propylene-diene monomer (EPDM) rubber, sulfonated EPDM,fluorinated rubbers, styrene butadiene rubber (SBR), polyacrylonitrile(PAN), polymethyl methacrylate (PMMA), polyacrylic acid (PAA),cross-linked polyethylene (PEX, XLPE), polyethylene (PE), polyethyleneterephthalate (PET), polyphenyl ether (PPE), polyvinyl chloride (PVC),polyvinylidene chloride (PVDC), polyamide (PA), polyimide (PI),polycarbonate (PC), polytetrafluoroethylene (PTFE), polystyrene (PS),polyurethane (PU), polyester (PE), acrylonitrile butadiene styrene(ABS), polyoxymethylene (POM), polysulfone (PES), styrene-acrylonitrile(SAN), ethylene vinyl acetate (EVA), styrene maleic anhydride (SMA),combinations of these, and other inert polymers that have elasticmodulus between 1 E-5 GPa and 10 GPa), and are inert in the battery. Inparticular, similarly to the filler particles above, the concentrationsthese materials can be chosen by engineering design of properties inorder to achieve a predetermined compressibility of the cathodestructure. For example, in one embodiment, to obtain a cathode structurewith a cathode active material layer having a relatively highcompressibility, polymers with a relatively low elastic modulus (Young'sModulus) can be provided in relatively high concentrations in thecathode active material layer. In another embodiment, the polymericmaterial is a copolymer or blend of two or more of the aforementionedpolymers.

In one embodiment, members of the population of cathode structure 112have a compressibility that imparts good performance duringcharging/discharging cycles in the secondary battery. For example, inone embodiment, one or more members of the population cathode structures112 may exhibit a compression, as defined by a(Dimension₁−Dimension₂)/(Dimension₁)×100, where Dimension₁ is adimension of the cathode structures (such as width or cross-section) inthe discharged state), and Dimension₂ is a dimension of the cathodestructure in the charged state, of at least 5% at a pressure of at least0.7 MPa (100 psi). By way of further example, one or more members of thepopulation of the cathode structure may exhibit a compression of atleast 10% at a pressure of 0.7 MPa (100 psi). By way of further example,one or more members of the population of cathode structures may exhibita compression of at least 25% at a pressure of 0.7 MPa (100 psi). By wayof further example, one or more members of the population of cathodestructures may exhibit a compression of at least 5% at a pressure of 70MPa (10,000 psi). By way of further example, one or more members of thepopulation of cathode structures may exhibit a compression of at least10% at a pressure of 70 MPa (10,000 psi). For example, in oneembodiment, one or more members of the population of cathode structures112 may exhibit a compression in the range of from 5% to 75% at apressure of 0.7 MPa (100 psi). By way of further example, in oneembodiment, one or more members of the population of cathode structures112 may exhibit a compression in the range of from 0.5% to 75% at apressure of 70 MPa (10,000 psi). By way of further example, in oneembodiment, one or more members of the population of cathode structures112 may exhibit a compression in the range of from 20% to 50% at apressure of 0.7 MPa (100 psi). By way of further example, in oneembodiment, one or more members of the population of cathode structures112 may exhibit a compression in the range of from 20% to 50% at apressure of 70 MPa (10,000 psi).

In one embodiment, the members of the population of cathode structures112 have a cathode active material layer 138 with filler particles thatare both compressible and elastic. That is, the filler particles cancomprise particles such as polymeric beads or other materials that cancompress with compression of cathode structure, and that have anelasticity that allows the particles to at least partially recover theirshape prior to compression. In one embodiment, the filler particleshaving a predetermined level of elasticity may help facilitate expansionof the cathode structures during discharge of the secondary battery,without excessively inhibiting compression of the cathode structuresduring charging of the secondary battery. The filler particles may alsocomprise an elasticity as measured according to Young's Modulus in therange of from 0.1 GPa to 10 Gpa, such as from 0.1 to 4.1 GPa, and evenfrom 2.5 GPa to 10 Gpa.

In one embodiment, the members of the population of cathode structures112 have a cathode active material layer 138 with filler particles thatare incompressible and porous. The filler particles can comprisestructures such as hollow micro-spheres, micro-fibers, micro-tubes,micro-cylinders, micro-skeletons, and other microscopic and nanoscopicobject shapes and sizes that are compatible in the battery. The porousfiller particles can comprise an incompressible material such as forexample a porous ceramic material, or a porous material having a hardceramic cell, that resists compression, while also providing a porousinterior. These porous, incompressible particles can be used aselectrolyte reservoirs in the matrix of the electrode. When theelectrode is in its compressed form, the electrolyte stored in theporosity of these particles can act towards reducing the ionicresistance of the matrix electrode.

According to one aspect, the filler materials that act as electrolytereservoirs can be made from ceramics, polymers, metals, metal oxides, orother compatible materials. The amount, size, shape, and materialproperties of the filler particles can be tailored for the particularuse and the pressures generated by the battery during operation.

In one embodiment, the compressibility and porosity of the fillermaterial can be tailored to the application and the pressures generatedby the battery during operation. In one instance, the filler particlesare incompressible under the pressures applied by the battery duringoperation, and the electrolyte stored inside the filler particles do notappreciably change in volume during charge and discharge. In otherembodiments, the filler material is less compressible than the electrodematrix, so that even though the electrolyte volume in the fillerparticle is lower in the compressed state than in the uncompressedstate, it is greater than the electrolyte volume in the matrix, thereby,providing ionic conductivity.

The porosity of the filler material designed for use as an electrolytereservoir is preferably high in order to maximize the amount ofelectrolyte in the particle during battery operation. Preferably, theporosity may be greater than 60%, such as greater than 70%, greater than80%, and even greater than 90% by volume fo the filler material.According to one aspect, the pore sizes of the filler material may begenerally greater than 5 nm, such as greater than 10 nm, and evengreater than 50 nm, in order to facilitate ion transport.

The filler materials that are used to constitute an electrolytereservoir may, in one embodiment, be made of materials that have aelasticity according to the Young's modulus of greater than 10 GPa, suchgreater than 50 GPa, and even greater than 100 Gpa.

In one embodiment, the secondary battery 102 having the members of theanode and cathode structure population 110, 112 that are capable ofexpanding and/or contracting, such as inverse relation to one another,may be capable of providing synergistic effects in terms ofsimultaneously imparting both a relatively high areal capacity and/orenergy density, and a relatively high rate of discharge (e.g., asmeasured by the rate capability) of the secondary battery. For example,the secondary battery 102 may in certain aspects be capable ofpreserving porosity of the cathod structure 110 under compressionthereof. Without being limited to any one particular theory, it isbelieved that the expansion/contraction of the members of the populationof cathode structures 112 upon discharge/charge of the secondary battery102 allows for cathode structures 112 to be used that provide arelatively high areal capacity, without sacrificing the rate at whichdischarge of the secondary battery can occur. By way of clarification,it is noted that the areal capacity of a secondary battery 102 may berelated to the relatively high cathode volume per unit geometrical area(i.e., the cathode active material volume) that can be provided. Ingeneral, a relatively higher volume of cathode per unit geometrical areawill result in a relatively higher areal capacity. However, batterieswith cathodes having a relatively high volume, such as those having arelatively high thickness in the longitudinal direction, may alsoexperience a reduction in discharge as compared to thinner cathodes, dueto the larger amount of cathode active material that is present in theinterior of the cathode as opposed to at a cathode surface. However,without being limited by any theory, it is believed that theexpansion/contraction of the cathode structures 112, and the change inporosity of the cathode active material layers 138 that occurs with theexpansion/contraction, may allow for a rate of discharge that at leastpartially compensates for any reduction that might otherwise be observedwith a cathode structure 112 having a relatively high volume. That is,it is hypothesized that the expansion of the cathode and increasedporosity in the cathode during discharge may facilitate contact of theelectrolyte with the cathode active material, even at more interiorregions of the cathode, thereby facilitating an increased dischargerate. Accordingly, aspects of the present disclosure may allow for arelatively large volume of cathode active material to be provided (withrespect to the total volume of cathode structures, anode structures, andseparators), while maintaining a relatively high rate of discharge, andthus a high rate capability of the secondary battery.

For example, in one embodiment, the areal capacity of the secondarybattery may be determined as the capacity of the battery per medianopposing surface area of members of the anode structure population ofthe battery, where the opposing surface area is the area of the portionof the anode surface that faces a cathode surface directly adjacent tothe anode in the stacking direction. The areal capacity may be measuredin units of mA·h/cm². For example, referring to FIG. 1D, the opposingsurface area O_(A) may be that portion of the anode surface area betweenpoints 126 a and 126 b along the length LA of the anode, multiplied bythe height H_(A), where the point 126 b is a distal end of the anode,and the point 126 a is a point just short of the base of the anode,located across from the distal end of the facing cathode 112, and thus126 a and 126 b mark the end of the surface region of the anode thatdirectly faces the opposing cathode 112 surface. Accordingly, in oneembodiment, the areal capacity of the secondary battery is at least 3mA·h/cm² at 0.1 C. By way of further example, in one embodiment, theenergy density of the secondary battery is at least 5 mA·h/cm² at 0.1 C.By way of further example, in one embodiment, the energy density of thesecondary battery is at least 8 mA·h/cm² at 0.1 C. By way of furtherexample, in one embodiment, the energy density of the secondary batteryis at least 10 mA·h/cm² at 0.1 C. By way of further example, in oneembodiment, the energy density of the secondary battery is at least 15mA·h/cm² at 0.1 C. By way of further example, in one embodiment, theenergy density of the secondary battery is at least 20 mA·h/cm² at 0.1C. By way of further example, in one embodiment, the energy density ofthe secondary battery is at least 25 mA·h/cm² at 0.1 C. For example, inone embodiment, the energy density of the secondary battery 102 is in arange of from 3 to 50 mA·h/cm² at 0.1 C By way of further example, inone embodiment, the energy density of the secondary battery 102 is in arange of from 5 to 25 mA·h/cm² at 0.1 C. By way of further example, inone embodiment, the energy density of the secondary battery 102 is in arange of from 8 to 20 mA·h/cm² at 0.1 C.

In one embodiment, the secondary battery 102 may provide a higherdischarge rate that can be quantified according to the rate capabilityof the secondary battery. The rate capability of the secondary batteryrefers to the ratio of the capacity of the secondary battery at a firstCrate to the capacity of the secondary battery at a second C-rate,expressed as a percentage. For example, the rate capability maycalculated according to Capacity₁/Capacity₂×100, where Capacity₁ is thecapacity for discharge at the first C-rate, such as a C-rate of 1 C, andCapactiy₂ is the capacity for discharge at a second C-rate, such as aCrate of C/10, and may be expressed as the calculated percentage for aspecified ratio C_(x)/C_(y), where C_(x) is the first C-rate, and C_(y)is the second C-rate. In particular, the rate capability metric mayserve as a measure of the efficiency of the rate of discharge of thesecondary battery when discharged at a higher rate as compared to alower rate. By way of clarification, it is noted that practice,increasing the speed of discharge of a secondary battery results in thegeneration of impedances and other forces that can build up to oppose tohigher current. Accordingly, the rate capability may be a measure of thechange in capacity that occurs due to changes in discharge rate. In oneembodiment, the secondary battery may be capable of providing a ratecapability of 1 C:C/10 of at least 75%. By way of further example, thesecondary battery may be capable of providing a rate capability of 1C:C/10 of at least 80%. By way of further example, the secondary batterymay be capable of providing a rate capability of 1 C:C/10 of at least90%. By way of further example, the secondary battery may be capable ofproviding a rate capability of 1 C:C/10 of at least 95%. By way offurther example, the secondary battery may be capable of providing a 2C:C/10 rate of at least 75%. By way of further example, the secondarybattery may be capable of providing a rate capability of 2 C:C/10 of atleast 80%. By way of further example, the secondary battery may becapable of providing a rate capability of 2 C:C/10 of at least 90%. Byway of further example, the secondary battery may be capable ofproviding a rate capability of 2 C:C/10 of at least 95%. By way offurther example, the secondary battery may be capable of providing a 5C:C/10 rate of at least 75%. By way of further example, the secondarybattery may be capable of providing a rate capability of 5 C:C/10 of atleast 80%. By way of further example, the secondary battery may becapable of providing a rate capability of 5 C:C/10 of at least 90%. Byway of further example, the secondary battery may be capable ofproviding a rate capability of 5 C:C/10 of at least 95%.

In one embodiment, the secondary battery has an areal capacity of atleast 3 mA·h/cm² at 0.1 C, and a rate capability of 1 C/0.1 C of atleast 75%. For example, in one embodiment, the secondary battery mayhave an areal capacity of at least 5 mA·h/cm² at 0.1 C, and a ratecapability of 1 C/0.1 C of at least 75%, such as a rate capability of 1C/0.1 C of at least 80% and even at least 90%, such as 95%. By way offurther example, in one embodiment, the secondary battery may have anareal capacity of at least 8 mA·h/cm² at 0.1 C, and a rate capability of1 C/0.1 C of at least 75%, such as a rate capability of 1 C/0.1 C of atleast 80% and even at least 90%, such as 95%. By way of further example,in one embodiment, the secondary battery may have an areal capacity ofat least 10 mA·h/cm² at 0.1 C, and a rate capability of 1 C/0.1 C of atleast 75%, such as a rate capability of 1 C/0.1 C of at least 80% andeven at least 90%, such as 95%. By way of further example, in oneembodiment, the secondary battery may have an areal capacity of at least15 mA·h/cm² at 0.1 C, and a rate capability of 1 C/0.1 C of at least75%, such as a rate capability of 1 C/0.1 C of at least 80% and even atleast 90%, such as 95%. By way of further example, in one embodiment,the secondary battery may have an areal capacity of at least 20 mA·h/cm²at 0.1 C, and a rate capability of 1 C/0.1 C of at least 75%, such as arate capability of 1 C/0.1 C of at least 80% and even at least 90%, suchas 95%. By way of further example, in one embodiment, the secondarybattery may have an areal capacity of at least 25 mA·h/cm² at 0.1 C, anda rate capability of 1 C/0.1 C of at least 75%, such as a ratecapability of 1 C/0.1 C of at least 80% and even at least 90%, such as95%.

In yet another embodiment, without being limited to any particulartheory, it is believed that the electrode assembly 106 having theexpanding/contracting cathode structures 112 may be capable of providingan electrolyte pumping effect that increases movement and flow ofelectrolyte to the cathode active material in the cathode structures andhelps to maintain a high rate of discharge of the secondary battery 102having the cathode structures 112. By way of clarification, and withoutbeing limited to any one particular theory, it is noted that a volumeoccupied by the electrolyte in the secondary battery 102 includes thevolume occupied by the electrolyte in between members of the populationof cathode and anode structures 112, 110, and also includes any openvolume due to the presence of pores, etc., in the members of thepopulation of anode structures 110, and the open volume in the membersof the population of cathode structures 112, resulting from the porositythereof. As the secondary battery 102 is charged, any pores in themembers of the population of anode structures 110 become increasinglyfilled with intercalated and/or inter-alloyed carrier ions, such that avolume of electrolyte occupying the members of the population of anodestructures 110 decreases. Furthermore, the increase in size of themembers of the population of anode structures 110 due to thisintercalation and/or inter-alloying may compress the members of thepopulation of cathode structures 112, as discussed above, therebyreducing the open pore volume in the cathode structure members such thata volume of electrolyte occupying the cathode structures 112 decreaseswhen the secondary battery 102 is being charged. Conversely, dischargingof the secondary battery 102 may result in de-intercalation and/orde-alloying of the carrier ions, to provide more available volume in theanode structure, and may also result in expansion of the cathodestructures, which can increase the porosity and the available volume forelectrolyte in the pores/open volume of the members of the cathodestructure population. That is, the electrolyte may occupy a volume V₁ inthe pores of the members of the population of cathode structures 112 inthe charged state that is smaller than a volume V₂ in the pores of themembers of the population of cathode structures 112 in the dischargedstate. By way of explanation, and not being limited by any theory, it isbelieved that this change in available volume (between V₁ and V₂) forthe electrolyte in the members of the population of cathode structures112 (and even in the anode structure population) in cycling betweencharged and discharged states may provide an electrolyte pumping effectwhereby the electrolyte is agitated and/or “pumped” into and about thepores of the cathode active material layer 138 during cycling. Thus, the“pumping” of the electrolyte into and about pores of the cathode activematerial layer 138 may bring the electrolyte into contact with cathodeactive material, and can enhance the rate of discharge of the cathodeactive material layer due to the increased contact of the cathode activematerial with the electrolyte during the discharge process. The volumeV₂ of the pores of the members of the population of cathode structures112 in the discharged state may be related to the porosity of thecathode active material layer 138 in the discharged state, and thevolume V₁ of the pores of the members of the population of cathodestructures 112 in the charged state may be related to the porosity ofthe cathode active material layer 138 in the charged state. In oneembodiment, a ratio V₂:V1 of the volume of the cathode active materiallayer 138 available for the electrolyte in the discharged state to thevolume in the charged state may be at least 1.1:1. For example, in oneembodiment, the ratio V₂:V₁ may be at least 1.5:1. For example, in oneembodiment, the ratio V₂:V₁ may be at least 2:1. For example, in oneembodiment, the ratio V₂:V₁ may be at least 5:1. By way of furtherexample, in one embodiment the ratio V₂:V₁ may be at least 10:1. By wayof yet a further example, in one embodiment the ratio V₂:V₁ may be atleast 15:1. For example, the ratio V₂ to may be in the range of from1.1:1 to 30:1, such as from 1.5:1 to 20:1, and even from 3:1 to 15:1. Inyet another embodiment, porous filler particles may also be provided tofacilitate a predetermined pore volume in one or more of the chargeand/or discharged states.

In yet another embodiment, a method of formation of a secondary batteryfor cycling between charged and discharged states may be provided.According to one aspect, the method of formation may comprise at leastone initial formation charging step, in which the secondary battery 102is charged such that members of the population of anode structures 110expand, with the result that the expanding anode structures 110 compressmembers of the population of cathode structures 112. Generally speaking,the formation stage may involve one or more initial charging steps thatare performed under conditions that re-arrange and/or optimize internalstructures and morphologies, such that the secondary battery can becharged up to its rated capacity. For example, the formation stage mayinvolve one or more charging steps performed under carefully controlledconditions of current, temperature and duration, for example to minimizeimpedance in the secondary battery and optimize contact betweenelectrolyte and electrodes. In one embodiment, during the formationstage, the members of the population of anode structures 110 maycompress the compressible layers 138 of cathode active material to asize that is less than an original size of the cathode active materiallayers 138 prior to the initial formation stage. The initial formationstage may thus provide for in situ formation of members of thepopulation of cathode structures 112 having a predetermined size,cross-sectional area and/or volume, as well as a predetermined density,porosity, and/or volume % of the cathode active material in the cathodeactive material layers 138 of the cathode structure population members.In one embodiment, the initial formation stage compresses a subset ofthe population of cathode structures 112 such that the cross-sectionalarea decreases from an initial cross-sectional area C_(i) prior to theinitial formation step to a post-formation cross-sectional area C_(f)after the initial formation stage that is less than 95% of the initialcross-sectional area C_(i). By way of further example, in oneembodiment, the initial formation stage compresses a subset of thepopulation of cathode structures 112 such that the cross-sectional areadecreases from an initial cross-sectional area C_(i) prior to theinitial formation stage to a post-formation cross-sectional area C_(f)after the initial formation stage that is less than 90% of the initialcross-sectional area C_(i). By way of further example, in oneembodiment, the initial formation stage compresses a subset of thepopulation of cathode structures 112 such that the cross-sectional areadecreases from an initial cross-sectional area C_(i) prior to theinitial formation stage to a post-formation cross-sectional area C_(f)after the initial formation stage that is less than 80% of the initialcross-sectional area C_(i). By way of further example, in oneembodiment, the initial formation stage may compress a subset of thepopulation of cathode structures 112 such that the cross-sectional areadecreases from an initial cross-sectional area C_(i) prior to theinitial formation stage to a post-formation cross-sectional area C_(f)after the initial formation stage that is less than 70% of the initialcross-sectional area C_(i). Generally, the post-formationcross-sectional area C_(f) will be at least 25% of the initialcross-sectional area C_(i). For example, the initial formation step maycompress a subset of the population of the cathode structures 112 to across-sectional area C_(f) that is in the range of from 25% to 95% ofC_(i), such as in a range of from 30% to 80% of C_(i), and even in arange of from 40% to 60% of C_(i). Furthermore, according to oneembodiment, a median cross-sectional area, as measured either accordingto MA_(C) (e.g., a median of cross-sectional areas for more than onecathode member), ML_(C) (e.g., a median of cross-sectional areas atdifferent longitudinal planes long a cathode member), and/or MO_(C)(e.g., a median of MAc and MLc), as discussed above, may be used todetermine the extent of compression of a subset of the population ofcathode structures during the initial formation, and may exhibit mediancross-sectional areas post-formation as a % of the mediancross-sectional areas pre-formation that are similar to and/or the sameas the ranges for C_(f) as a % of C_(i) above.

Also, the formation stage may result in the increase in size of themembers of the population of anode structures. For example, the initialcross-sectional area A_(i) of a subset of the population of anodestructures may increase to a post-formation cross-sectional area A_(f)that provides a ratio of A_(f):A_(i) that is at least 1.1:1, such as atleast 1.3:1, and even at least 1.5:1. For example, the ratio A_(f):A_(i)may be at least 2:1, and may even be at least 3:1, such as at least 4:1,and even at least 5:1. For example, a cross-sectional area C_(i) of thesubset of the population of cathode structures before the initialformation step may be in the range of from 800 μm² to 8×10⁶ μm², such asfrom 1000 μm² to 5×10⁶ μm², and even from 1500 μm² to 3×10⁶ μm². Bycontrast, the cross-sectional area C_(f) of the subset of the populationof cathode structures after the initial formation step may be in therange of from 3500 μm² to 8×10⁶ μm², such as from 4000 μm² to 5.05×10⁶μm², and even from 500 μm² to 3×10⁶. Furthermore, according to oneembodiment, a median cross-sectional area, as measured either accordingto MA_(A) (e.g., a median of cross-sectional areas for more than oneanode member), ML_(A) (e.g., a median of cross-sectional areas atdifferent longitudinal planes long an anode member), and/or MO_(A)(e.g., a median of MA_(A) and ML_(A)), as discussed above, may be usedto determine the extent of expansion of a subset of the population ofanode structures during the initial formation stage, and may exhibitmedian cross-sectional areas post-formation as a % of the mediancross-sectional areas pre-formation that are similar to and/or the sameas the ranges for the ratio of A_(f) to A_(i) as above.

In yet another embodiment, the initial formation stage may comprisecharging the secondary battery 102 to compress the cathode activematerial layers 138 to decrease the porosity thereof, and/or to increasea volume % of the cathode active material layers 138 occupied byparticles of cathode active material and/or filler (e.g., to densify thecathode active material layers). By way of example, in one embodiment,the volume % of particles in the cathode active material layers 138before the initial formation stage may be no more than 50%, such as nomore than 30% and even no more than 25%. By contrast, a volume % ofparticles in the cathode active material layers 138 after the initialformation stage may be at least 60%, such as at least 75% and even atleast 85%, such as at least 95%.

According to yet another embodiment, the initial formation stage maycomprise charging the secondary battery 102 such that the members of thepopulation of anode structures 110 expand and compress the microporousseparator 130 against the cathode structures 112 and/or anodestructures, at a pressure that causes the microporous separator to atleast partially adhere to members of the populations of cathode andanode structures. That is, in a case where the microporous separator 130comprises a polymeric or other material capable of at least partiallyplasticizing and/or otherwise adhering to members of the populations ofcathode structures 112 and/or anode structure 110, the compression ofthe microporous separator 130 against the members can cause theseparator and members to at least partially adhere to each other. In oneembodiment, the at least partial adhesion of the microporous separatorto the cathode structure and/or anode structure members can cause thecathode structure members to expand upon discharge of the secondarybattery 102. By way of clarification, it is noted that charging of thesecondary battery expands the members of the population of anodestructures 110, and this expansion may also stretch portions of anelastic microporous separator 130 that are adjacent to the anodestructure members. Furthermore, when the members of the population ofanode structures 110 contract during discharge of the secondary battery102, the elastic microporous separator may also contract back to a morerelaxed state, such as substantially conformally with the contractingprofile of the anode structure population members 110. However, as theseparator 130 is at least partially adhered to the members, thecontraction of the separator also exerts a force to pull a surface ofthe members of the population of cathode structures 112 that is at leastpartially adhered to the microporous separator, thereby causing themembers to expand in size. That is, the at least partial adhesion of theseparator 130 to the members of the population of cathode structures 112and/or anode structure 110 may thus cause the cathode structurepopulation members 112 to expand in concert with contraction of themembers of the population of anode structures 110 during discharge ofthe secondary battery 102, for example such that the cathode structurepopulation members 112 expand in size in a manner that is inverselyrelated to the contraction in size of the anode structure populationmembers 110. In one embodiment, the initial formation stage comprisescharging the secondary battery 102 such that the members of thepopulation of anode structures 110 expand and compress the microporousseparator 130 against the members of the population of cathodestructures 112 at a pressure sufficient to at least partially fuse apolymeric material of the microporous separator at a surface of themicroporous separator 130, to a polymeric matrix material at acontacting surface of the cathode active material layer 138 of thecathode structure 112, and to a contacting surface of the anodestructure 110, such that the cathode active material layer 138 expandsand/or contracts in concert with flexing and/or contracting of theseparator, during cycling of the secondary battery 102.

In one embodiment, the initial formation stage comprises charging thesecondary battery such that members of the population of anodestructures expand and exert a pressure to compress the microporousseparators 130 against members of the population of cathode structuresand/or anode structures at a pressure of at least 1,000 psi. In anotherembodiment, the microporous separators are compressed against themembers of the cathode structure population and/or anode structurepopulation during the initial formation stage at a pressure of at least3,000 psi. In yet another embodiment, the microporous separators arecompressed against the members of the population of cathode structuresand/or anode structures during the initial formation stage at a pressureof at least 5,000 psi. In yet another embodiment, the microporousseparators are compressed against the members of the population ofcathode structures and/or anode structures during the initial formationstage at a pressure of at least 10,000 psi.

Embodiments of the energy storage device 100 such as the secondarybattery 102 and components thereof, having the compressible cathodestructures 112, are described in further detail below.

Electrode Assembly

Referring again to FIGS. 1A-1B, in one embodiment, an interdigitatedelectrode assembly 106 includes a population of anode structures 110, apopulation of cathode structures 112, and an electrically insulatingmicroporous separator 130 electrically insulating the anode structures110 from the cathode structures 112. In one embodiment, the anodestructures 110 comprise an anode active material layer 132, an anodebackbone 134 that supports the anode active material layer 132, and ananode current collector 136, which may be an ionically porous currentcollector to allow ions to pass therethrough, as shown in the embodimentdepicted in FIG. 7. Similarly, in one embodiment, the cathode structures112 comprise a cathode active material layer 138, a cathode currentcollector 140, and a cathode backbone 141 that supports one or more ofthe cathode current collector 140 and/or the cathode active materiallayer 138, as shown for example in the embodiment depicted in FIG. 7.The electrically insulating microporous separator 130 allows carrierions to pass therethrough during charge and/or discharge processes, totravel between the anode structures 110 and cathode structures 112 inthe electrode assembly 106. Furthermore, it should be understood thatthe anode and cathode structures 110 and 112, respectively, are notlimited to the specific embodiments and structures described herein, andother configurations, structures, and/or materials other than thosespecifically described herein can also be provided to form the anodestructures 110 and cathode structures 112. For example, the anode andcathode structures 110, 112 can be provided in a form where thestructures are substantially absent any anode and/or cathode backbones134, 141, such as in a case where the region of the anode and/or cathodestructures 110, 112 that would contain the backbones is instead made upof anode active material and/or cathode active material.

According to the embodiment as shown in FIGS. 1A-1B, the members of theanode and cathode structure populations 110 and 112, respectively, arearranged in alternating sequence, with a direction of the alternatingsequence corresponding to the stacking direction D. The electrodeassembly 106 according to this embodiment further comprises mutuallyperpendicular longitudinal, transverse, and vertical axes, with thelongitudinal axis A_(EA) generally corresponding or parallel to thestacking direction D of the members of the electrode andcounter-electrode structure populations. As shown in the embodiment inFIG. 1A, the longitudinal axis A_(EA) is depicted as corresponding tothe Y axis, the transverse axis is depicted as corresponding to the Xaxis, and the vertical axis is depicted as corresponding to the Z axis.

Further, the electrode assembly 106 has a maximum width W_(EA) measuredin the longitudinal direction (i.e., along the y-axis), a maximum lengthL_(EA) bounded by the lateral surface and measured in the transversedirection (i.e., along the x-axis), and a maximum height H_(EA) alsobounded by the lateral surface and measured in the vertical direction(i.e., along the z-axis). The maximum width W_(EA) can be understood ascorresponding to the greatest width of the electrode assembly 106 asmeasured from opposing points of the longitudinal end surfaces 116, 118of the electrode assembly 106 where the electrode assembly is widest inthe longitudinal direction. For example, referring to the embodiment ofthe electrode assembly 106 in FIG. 1A, the maximum width W_(EA) can beunderstood as corresponding simply to the width of the assembly 106 asmeasured in the longitudinal direction. However, referring to theembodiment of the electrode assembly 106 shown in FIG. 5H, it can beseen that the maximum width W_(EA) corresponds to the width of theelectrode assembly as measured from the two opposing points 300 a, 300b, where the electrode assembly is widest in the longitudinal direction,as opposed to a width as measured from opposing points 301 a, 301 bwhere the electrode assembly 106 is more narrow. Similarly, the maximumlength L_(EA) can be understood as corresponding to the greatest lengthof the electrode assembly as measured from opposing points of thelateral surface 142 of the electrode assembly 106 where the electrodeassembly is longest in the transverse direction. Referring again to theembodiment in FIG. 1A, the maximum length L_(EA) can be understood assimply the length of the electrode assembly 106, whereas in theembodiment shown in FIG. 5H, the maximum length L_(EA) corresponds tothe length of the electrode assembly as measured from two opposingpoints 302 a, 302 b, where the electrode assembly is longest in thetransverse direction, as opposed to a length as measured from opposingpoints 303 a, 303 b where the electrode assembly is shorter. Alongsimilar lines, the maximum height H_(EA) can be understood ascorresponding to the greatest height of the electrode assembly asmeasured from opposing points of the lateral surface 143 of theelectrode assembly where the electrode assembly is highest in thevertical direction. That is, in the embodiment shown in FIG. 1A, themaximum height H_(EA) is simply the height of the electrode assembly.While not specifically depicted in the embodiment shown in FIG. 5H, ifthe electrode assembly had different heights at points across one ormore of the longitudinal and transverse directions, then the maximumheight H_(EA) of the electrode assembly would be understood tocorrespond to the height of the electrode assembly as measured from twoopposing points where the electrode assembly is highest in the verticaldirection, as opposed to a height as measured from opposing points wherethe electrode assembly is shorter, as analogously described for themaximum width W_(EA) and maximum length L_(EA). The maximum lengthL_(EA), maximum width W_(EA), and maximum height H_(EA) of the electrodeassembly 106 may vary depending upon the energy storage device 100 andthe intended use thereof. For example, in one embodiment, the electrodeassembly 106 may include maximum lengths L_(EA), widths W_(EA), andheights H_(EA) typical of conventional secondary battery dimensions. Byway of further example, in one embodiment, the electrode assembly 106may include maximum lengths L_(EA), widths W_(EA), and heights H_(EA)typical of thin-film battery dimensions.

In some embodiments, the dimensions L_(EA), W_(EA), and H_(EA) areselected to provide an electrode assembly 106 having a maximum lengthL_(EA) along the transverse axis (X axis) and/or a maximum width W_(EA)along the longitudinal axis (Y axis) that is longer than the maximumheight H_(EA) along the vertical axis (Z axis). For example, in theembodiment shown in FIG. 1A, the dimensions L_(EA), W_(EA), and H_(EA)are selected to provide an electrode assembly 106 having the greatestdimension along the transverse axis (X axis) that is orthogonal withelectrode structure stacking direction D, as well as along thelongitudinal axis (Y axis) coinciding with the electrode structurestacking direction D. That is, the maximum length L_(EA) and/or maximumwidth W_(EA) may be greater than the maximum height H_(EA). For example,in one embodiment, a ratio of the maximum length L_(EA) to the maximumheight H_(EA) may be at least 2:1. By way of further example, in oneembodiment a ratio of the maximum length L_(EA) to the maximum heightH_(EA) may be at least 5:1. By way of further example, in oneembodiment, the ratio of the maximum length L_(EA) to the maximum heightH_(EA) may be at least 10:1. By way of further example, in oneembodiment, the ratio of the maximum length L_(EA) to the maximum heightH_(EA) may be at least 15:1. By way of further example, in oneembodiment, the ratio of the maximum length L_(EA) to the maximum heightH_(EA) may be at least 20:1. The ratios of the different dimensions mayallow for optimal configurations within an energy storage device tomaximize the amount of active materials, thereby increasing energydensity.

In some embodiments, the maximum width W_(EA) may be selected to providea width of the electrode assembly 106 that is greater than the maximumheight H_(EA). For example, in one embodiment, a ratio of the maximumwidth W_(EA) to the maximum height H_(EA) may be at least 2:1. By way offurther example, in one embodiment, the ratio of the maximum widthW_(EA) to the maximum height H_(EA) may be at least 5:1. By way offurther example, in one embodiment, the ratio of the maximum widthW_(EA) to the maximum height H_(EA) may be at least 10:1. By way offurther example, in one embodiment, the ratio of the maximum widthW_(EA) to the maximum height H_(EA) may be at least 15:1. By way offurther example, in one embodiment, the ratio of the maximum widthW_(EA) to the maximum height H_(EA) may be at least 20:1.

According to one embodiment, a ratio of the maximum width W_(EA) to themaximum length L_(EA) may be selected to be within a predetermined rangethat provides for an optimal configuration. For example, in oneembodiment, a ratio of the maximum width W_(EA) to the maximum lengthL_(EA) may be in the range of from 1:5 to 5:1. By way of furtherexample, in one embodiment a ratio of the maximum width W_(EA) to themaximum length L_(EA) may be in the range of from 1:3 to 3:1. By way ofyet a further example, in one embodiment a ratio of the maximum widthW_(EA) to the maximum length L_(EA) may be in the range of from 1:2 to2:1.

In the embodiment as shown in FIG. 1A, the electrode assembly 106 hasthe first longitudinal end surface 116 and the opposing secondlongitudinal end surface 118 that is separated from the firstlongitudinal end surface 116 along the longitudinal axis A_(EA). Theelectrode assembly 106 further comprises a lateral surface 142 that atleast partially surrounds the longitudinal axis A_(EA), and thatconnects the first and second longitudinal end surfaces 116, 118. In oneembodiment, the maximum width W_(EA) is the dimension along thelongitudinal axis A_(EA) as measured from the first longitudinal endsurface 116 to the second longitudinal end surface 118. Similarly, themaximum length L_(EA) may be bounded by the lateral surface 142, and inone embodiment, may be the dimension as measured from opposing first andsecond regions 144, 146 of the lateral surface 142 along the transverseaxis that is orthogonal to the longitudinal axis. The maximum heightH_(EA), in one embodiment, may be bounded by the lateral surface 142 andmay be measured from opposing first and second regions 148, 150 of thelateral surface 142 along the vertical axis that is orthogonal to thelongitudinal axis.

For the purposes of clarity, only four anode structures 110 and fourcathode structures 112 are illustrated in the embodiment shown in FIG.1A. For example, the alternating sequence of members of the anode andcathode structure populations 110 and 112, respectively, may include anynumber of members for each population, depending on the energy storagedevice 100 and the intended use thereof, and the alternating sequence ofmembers of the anode and cathode structure populations 110 and 112 maybe interdigitated, for example, as shown in FIG. 1A. By way of furtherexample, in one embodiment, each member of the population of anodestructures 110 may reside between two members of the population ofcathode structures 112, with the exception of when the alternatingsequence terminates along the stacking direction, D. By way of furtherexample, in one embodiment, each member of the population of cathodestructures 112 may reside between two members of the population of anodestructures 110, with the exception of when the alternating sequenceterminates along the stacking direction, D. By way of further example,in one embodiment, and stated more generally, the population of anodestructures 110 and the population of cathode structures 112 each have Nmembers, each of N-1 anode structure members 110 is between two cathodestructure members 112, each of N-1 cathode structure members 112 isbetween two anode structure members 110, and N is at least 2. By way offurther example, in one embodiment, N is at least 4. By way of furtherexample, in one embodiment, N is at least 5. By way of further example,in one embodiment, N is at least 10. By way of further example, in oneembodiment, N is at least 25. By way of further example, in oneembodiment, N is at least 50. By way of further example, in oneembodiment, N is at least 100 or more. In one embodiment, members of theanode and/or cathode populations extend sufficiently from an imaginarybackplane (e.g., a plane substantially coincident with a surface of theanode assembly) to have a surface area (ignoring porosity) that isgreater than twice the geometrical footprint (i.e., projection) of themembers in the backplane. In certain embodiments, the ratio of thesurface area of a non-laminar (i.e., three-dimensional) anode and/orcathode structure to its geometric footprint in the imaginary backplanemay be at least about 5, at least about 10, at least about 50, at leastabout 100, or even at least about 500. In general, however, the ratiowill be between about 2 and about 1000. In one such embodiment, membersof the anode population are non-laminar in nature. By way of furtherexample, in one such embodiment, members of the cathode population arenon-laminar in nature. By way of further example, in one suchembodiment, members of the anode population and members of the cathodepopulation are non-laminar in nature.

According to one embodiment, the electrode assembly 106 has longitudinalends 117, 119 at which the electrode assembly 106 terminates. Accordingto one embodiment, the alternating sequence of anode and cathodestructures 110, 112, respectively, in the electrode assembly 106terminates in a symmetric fashion along the longitudinal direction, suchas with anode structures 110 at each end 117, 119 of the electrodeassembly 106 in the longitudinal direction, or with cathode structures112 at each end 117, 119 of the electrode assembly 106, in thelongitudinal direction. In another embodiment, the alternating sequenceof anode 110 and cathode structures 112 may terminate in an asymmetricfashion along the longitudinal direction, such as with an anodestructure 110 at one end 117 of the longitudinal axis A_(EA), and acathode structure 112 at the other end 119 of the longitudinal axisA_(EA). According to yet another embodiment, the electrode assembly 106may terminate with a substructure of one or more of an anode structure110 and/or cathode structure 112 at one or more ends 117, 119 of theelectrode assembly 106. By way of example, according to one embodiment,the alternating sequence of the anode 110 and cathode structures 112 canterminate at one or more substructures of the anode 110 and cathodestructures 112, including an anode backbone 134, cathode backbone 141,anode current collector 136, cathode current collector 140, anode activematerial layer 132, cathode active material layer 138, and the like, andmay also terminate with a structure such as the separator 130, and thestructure at each longitudinal end 117, 119 of the electrode assembly106 may be the same (symmetric) or different (asymmetric). Thelongitudinal terminal ends 117, 119 of the electrode assembly 106 cancomprise the first and second longitudinal end surfaces 116, 118 thatare contacted by the first and second primary growth constraints 154,156 to constrain overall growth of the electrode assembly 106.

According to yet another embodiment, the electrode assembly 106 hasfirst and second transverse ends 145, 147 (see, e.g., FIG. 1A) that maycontact one or more electrode and/or counter electrode tabs 190, 192(see, e.g., FIG. 9) that may be used to electrically connect theelectrode and/or counter-electrode structures 110, 112 to a load and/ora voltage supply (not shown). For example, the electrode assembly 106can comprise an electrode bus 194 (see, e.g., FIG. 1A), to which eachanode structure 110 can be connected, and that pools current from eachmember of the population of electrode structures 110. Similarly, theelectrode assembly 106 can comprise a cathode bus 196 to which eachcathode structure 112 may be connected, and that pools current from eachmember of the population of cathode structures 112. The anode and/orcathode buses 194, 196 each have a length measured in direction D, andextending substantially the entire length of the interdigitated seriesof anode structures 110, 112. In the embodiment illustrated in FIG. 9,the anode tab 190 and/or cathode tab 192 includes anode tab extensions191, 193 which electrically connect with, and run substantially theentire length of anode and/or cathode bus 194, 196. Alternatively, theanode and/or cathode tabs 190, 192 may directly connect to the anodeand/or cathode bus 194, 196, for example, an end or positionintermediate thereof along the length of the buses 194, 196, withoutrequiring the tab extensions 191, 193. Accordingly, in one embodiment,the anode and/or cathode buses 194, 196 can form at least a portion ofthe terminal ends 145, 147 of the electrode assembly 106 in thetransverse direction, and connect the electrode assembly to the tabs190, 192 for electrical connection to a load and/or voltage supply (notshown). Furthermore, in yet another embodiment, the electrode assembly106 comprises first and second terminal ends 149, 153 disposed along thevertical (Z) axis. For example, according to one embodiment, each anode110 and/or cathode structure 112, is provided with a top and bottomcoating of separator material, as shown in FIG. 1A, where the coatingsform the terminal ends 149, 153 of the electrode assembly 106 in thevertical direction. The terminal ends 149, 153 that may be formed of thecoating of separator material can comprise first and second surfaceregions 148, 150 of the lateral surface 142 along the vertical axis thatcan be placed in contact with the first and second secondary growthconstraints 158, 160 to constrain growth in the vertical direction.

In general, the electrode assembly 106 can comprise longitudinal endsurfaces 116, 118 that are planar, co-planar, or non-planar. Forexample, in one embodiment the opposing longitudinal end surfaces 116,118 may be convex. By way of further example, in one embodiment theopposing longitudinal end surfaces 116, 118 may be concave. By way offurther example, in one embodiment the opposing longitudinal endsurfaces 116, 118 are substantially planar. In certain embodiments,electrode assembly 106 may include opposing longitudinal end surfaces116, 118 having any range of two-dimensional shapes when projected ontoa plane. For example, the longitudinal end surfaces 116, 118 mayindependently have a smooth curved shape (e.g., round, elliptical,hyperbolic, or parabolic), they may independently include a series oflines and vertices (e.g., polygonal), or they may independently includea smooth curved shape and include one or more lines and vertices.Similarly, the lateral surface 142 of the electrode assembly 106 may bea smooth curved shape (e.g., the electrode assembly 106 may have around, elliptical, hyperbolic, or parabolic cross-sectional shape) orthe lateral surface 142 may include two or more lines connected atvertices (e.g., the electrode assembly 106 may have a polygonalcross-section). For example, in one embodiment, the electrode assembly106 has a cylindrical, elliptic cylindrical, parabolic cylindrical, orhyperbolic cylindrical shape. By way of further example, in one suchembodiment, the electrode assembly 106 may have a prismatic shape,having opposing longitudinal end surfaces 116, 118 of the same size andshape and a lateral surface 142 (i.e., the faces extending between theopposing longitudinal end surfaces 116 and 118) beingparallelogram-shaped. By way of further example, in one such embodiment,the electrode assembly 106 has a shape that corresponds to a triangularprism, the electrode assembly 106 having two opposing triangularlongitudinal end surfaces 116 and 118 and a lateral surface 142consisting of three parallelograms (e.g., rectangles) extending betweenthe two longitudinal ends. By way of further example, in one suchembodiment, the electrode assembly 106 has a shape that corresponds to arectangular prism, the electrode assembly 106 having two opposingrectangular longitudinal end surfaces 116 and 118, and a lateral surface142 comprising four parallelogram (e.g., rectangular) faces. By way offurther example, in one such embodiment, the electrode assembly 106 hasa shape that corresponds to a pentagonal prism, hexagonal prism, etc.wherein the electrode assembly 106 has two pentagonal, hexagonal, etc.,respectively, opposing longitudinal end surfaces 116 and 118, and alateral surface comprising five, six, etc., respectively, parallelograms(e.g., rectangular) faces.

Referring now to FIGS. 5A-5H, several exemplary geometric shapes areschematically illustrated for electrode assembly 106. More specifically,in FIG. 5A, electrode assembly 106 has a triangular prismatic shape withopposing first and second longitudinal end surfaces 116, 118 separatedalong longitudinal axis A_(EA), and a lateral surface 142 including thethree rectangular faces connecting the longitudinal end surfaces 116,118, that are about the longitudinal axis A_(EA). In FIG. 5B, electrodeassembly 106 has a parallelopiped shape with opposing first and secondparallelogram longitudinal end surfaces 116, 118 separated alonglongitudinal axis A_(EA), and a lateral surface 142 including the fourparallelogram-shaped faces connecting the two longitudinal end surfaces116, 118, and surrounding longitudinal axis A_(EA). In FIG. 5C,electrode assembly 106 has a rectangular prism shape with opposing firstand second rectangular longitudinal end surfaces 116, 118 separatedalong longitudinal axis A_(EA), and a lateral surface 142 including thefour rectangular faces connecting the two longitudinal end surfaces 116,118 and surrounding longitudinal axis A_(EA). In FIG. 5D, electrodeassembly 106 has a pentagonal prismatic shape with opposing first andsecond pentagonal longitudinal end surfaces 116, 118 separated alonglongitudinal axis A_(EA), and a lateral surface 142 including the fiverectangular faces connecting the two longitudinal end surfaces 116, 118and surrounding longitudinal axis A_(EA). In FIG. 5E, electrode assembly106 has a hexagonal prismatic shape with opposing first and secondhexagonal longitudinal end surfaces 116, 118 separated alonglongitudinal axis A_(EA), and a lateral surface 142 including the sixrectangular faces connecting the two longitudinal end surfaces 116, 118and surrounding longitudinal axis A_(EA). In FIG. 5F, the electrodeassembly has a square pyramidal frustum shape with opposing first andsecond square end surfaces 116, 118 separated along longitudinal axisA_(EA), and a lateral surface 142 including four trapezoidal facesconnecting the two longitudinal end surfaces 116, 118 and surroundinglongitudinal axis A_(EA), with the trapezoidal faces tapering indimension along the longitudinal axis from a greater dimension at thefirst surface 116 to a smaller dimension at the second surface 118, andthe size of the second surface being smaller than that of the firstsurface. In FIG. 5G, the electrode assembly has a pentagonal pyramidalfrustum shape with opposing first and second square end surfaces 116,118 separated along longitudinal axis A_(EA), and a lateral surface 142including five trapezoidal faces connecting the two longitudinal endsurfaces 116, 118 and surrounding longitudinal axis A_(EA), with thetrapezoidal faces tapering in dimension along the longitudinal axis froma greater dimension at the first surface 116 to a smaller dimension atthe second surface 118, and the size of the second surface being smallerthan that of the first surface. In FIG. 5H, the electrode assembly 106has a pyramidal shape in the longitudinal direction, by virtue ofelectrode and counter-electrode structures 110, 112 having lengths thatdecrease from a first length towards the middle of the electrodeassembly 106 on the longitudinal axis, to second lengths at thelongitudinal ends 117, 119 of the electrode assembly 106.

Electrode Constraints

In one embodiment, a set of electrode constraints 108 is provided thatthat restrains overall macroscopic growth of the electrode assembly 106,as illustrated for example in FIGS. 1A-1B. The set of electrodeconstraints 108 may be capable of restraining growth of the electrodeassembly 106 along one or more dimensions, such as to reduce swellingand deformation of the electrode assembly 106, and thereby improve thereliability and cycling lifetime of an energy storage device 100 havingthe set of electrode constraints 108. As discussed above, without beinglimited to any one particular theory, it is believed that carrier ionstraveling between the anode structures 110 and cathode structures 112during charging and/or discharging of a secondary battery 102 can becomeinserted into anode active material, causing the anode active materialand/or the anode structure 110 to expand. This expansion of the anodestructure 110 can cause the electrodes and/or electrode assembly 106 todeform and swell, thereby compromising the structural integrity of theelectrode assembly 106, and/or increasing the likelihood of electricalshorting or other failures. In one example, excessive swelling and/orexpansion and contraction of the anode active material layer 132 duringcycling of an energy storage device 100 can cause fragments of anodeactive material to break away and/or delaminate from the anode activematerial layer 132, thereby compromising the efficiency and cyclinglifetime of the energy storage device 100. In yet another example,excessive swelling and/or expansion and contraction of the anode activematerial layer 132 can cause anode active material to breach theelectrically insulating microporous separator 130, thereby causingelectrical shorting and other failures of the electrode assembly 106.Accordingly, the set of electrode constraints 108 inhibit this swellingor growth that can otherwise occur with cycling between charged anddischarged states to improve the reliability, efficiency, and/or cyclinglifetime of the energy storage device 100.

According to one embodiment, the set of electrode constraints 108comprises a primary growth constraint system 151 to restrain growthand/or swelling along the longitudinal axis (e.g., Y-axis in FIGS.1A-1B) of the electrode assembly 106. In another embodiment, the set ofelectrode constraints 108 may include a secondary growth constraintsystem 152 that restrains growth along the vertical axis (e.g., Z-axisin FIG. 1). In yet another embodiment, the set of electrode constraints108 may include a tertiary growth constraint system 155 that restrainsgrowth along the transverse axis (e.g., X-axis in FIG. 4C). In oneembodiment, the set of electrode constraints 108 comprises primarygrowth and secondary growth constraint systems 151, 152, respectively,and even tertiary growth constraint systems 155 that operatecooperatively to simultaneously restrain growth in one or moredirections, such as along the longitudinal and vertical axis (e.g., Yaxis and Z axis), and even simultaneously along all of the longitudinal,vertical, and transverse axes (e.g., Y, Z, and X axes). For example, theprimary growth constraint system 151 may restrain growth that canotherwise occur along the stacking direction D of the electrode assembly106 during cycling between charged and discharged states, while thesecondary growth constraint system 152 may restrain swelling and growththat can occur along the vertical axis, to prevent buckling or otherdeformation of the electrode assembly 106 in the vertical direction. Byway of further example, in one embodiment, the secondary growthconstraint system 152 can reduce swelling and/or expansion along thevertical axis that would otherwise be exacerbated by the restraint ongrowth imposed by the primary growth constraint system 151. The tertiarygrowth constraint system 155 can also optionally reduce swelling and/orexpansion along the transverse axis that could occur during cyclingprocesses. That is, according to one embodiment, the primary growth andsecondary growth constraint systems 151, 152, respectively, andoptionally the tertiary growth constraint system 155, may operatetogether to cooperatively restrain multi-dimensional growth of theelectrode assembly 106.

Referring to FIGS. 6A-6B, an embodiment of a set of electrodeconstraints 108 is shown having a primary growth constraint system 151and a secondary growth constraint system 152 for an electrode assembly106. FIG. 6A shows a cross-section of the electrode assembly 106 in FIG.1 taken along the longitudinal axis (Y axis), such that the resulting2-D cross-section is illustrated with the vertical axis (Z axis) andlongitudinal axis (Y axis). FIG. 6B shows a cross-section of theelectrode assembly 106 in FIG. 1 taken along the transverse axis (Xaxis), such that the resulting 2-D cross-section is illustrated with thevertical axis (Z axis) and transverse axis (X axis). As shown in FIG.6A, the primary growth constraint system 151 can generally comprisefirst and second primary growth constraints 154, 156, respectively, thatare separated from one another along the longitudinal direction (Yaxis). For example, in one embodiment, the first and second primarygrowth constraints 154, 156, respectively, comprise a first primarygrowth constraint 154 that at least partially or even entirely covers afirst longitudinal end surface 116 of the electrode assembly 106, and asecond primary growth constraint 156 that at least partially or evenentirely covers a second longitudinal end surface 118 of the electrodeassembly 106. In yet another version, one or more of the first andsecond primary growth constraints 154, 156 may be interior to alongitudinal end 117, 119 of the electrode assembly 106, such as whenone or more of the primary growth constraints comprise an internalstructure of the electrode assembly 106. The primary growth constraintsystem 151 can further comprise at least one primary connecting member162 that connects the first and second primary growth constraints 154,156, and that may have a principal axis that is parallel to thelongitudinal direction. For example, the primary growth constraintsystem 151 can comprise first and second primary connecting members 162,164, respectively, that are separated from each other along an axis thatis orthogonal to the longitudinal axis, such as along the vertical axis(Z axis) as depicted in the embodiment. The first and second primaryconnecting members 162, 164, respectively, can serve to connect thefirst and second primary growth constraints 154, 156, respectively, toone another, and to maintain the first and second primary growthconstraints 154, 156, respectively, in tension with one another, so asto restrain growth along the longitudinal axis of the electrode assembly106.

According to one embodiment, the set of electrode constraints 108including the primary growth constraint system 151 may be capable ofrestraining growth of the electrode assembly 106 in the longitudinaldirection (i.e., electrode stacking direction, D) such that any increasein the Feret diameter of the electrode assembly in the longitudinaldirection over 20 consecutive cycles of the secondary battery is lessthan 20% between charged and discharged states. By way of furtherexample, in one embodiment the primary growth constraint system 151 maybe capable of restraining growth of the electrode assembly 106 in thelongitudinal direction such that any increase in the Feret diameter ofthe electrode assembly in the longitudinal direction over 30 consecutivecycles of the secondary battery is less than 20%. By way of furtherexample, in one embodiment the primary growth constraint system 151 maybe capable of restraining growth of the electrode assembly 106 in thelongitudinal direction such that any increase in the Feret diameter ofthe electrode assembly in the longitudinal direction over 50 consecutivecycles of the secondary battery is less than 20%. By way of furtherexample, in one embodiment the primary growth constraint system 151 maybe capable of restraining growth of the electrode assembly 106 in thelongitudinal direction such that any increase in the Feret diameter ofthe electrode assembly in the longitudinal direction over 80 consecutivecycles of the secondary battery is less than 20%. By way of furtherexample, in one embodiment the primary growth constraint system 151 maybe capable of restraining growth of the electrode assembly 106 in thelongitudinal direction such that any increase in the Feret diameter ofthe electrode assembly in the longitudinal direction over 100consecutive cycles of the secondary battery is less than 20%. By way offurther example, in one embodiment the primary growth constraint system151 may be capable of restraining growth of the electrode assembly 106in the longitudinal direction such that any increase in the Feretdiameter of the electrode assembly in the longitudinal direction over200 consecutive cycles of the secondary battery is less than 20%. By wayof further example, in one embodiment the primary growth constraintsystem 151 may be capable of restraining growth of the electrodeassembly 106 in the longitudinal direction such that any increase in theFeret diameter of the electrode assembly in the longitudinal directionover 300 consecutive cycles of the secondary battery is less than 20%.By way of further example, in one embodiment the primary growthconstraint system 151 may be capable of restraining growth of theelectrode assembly 106 in the longitudinal direction such that anyincrease in the Feret diameter of the electrode assembly in thelongitudinal direction such that any increase in the Feret diameter ofthe electrode assembly in the longitudinal direction over 500consecutive cycles of the secondary battery is less than 20%. By way offurther example, in one embodiment the primary growth constraint system151 may be capable of restraining growth of the electrode assembly 106in the longitudinal direction such that any increase in the Feretdiameter of the electrode assembly in the longitudinal direction over800 consecutive cycles of the secondary battery is less than 20%. By wayof further example, in one embodiment the primary growth constraintsystem 151 may be capable of restraining growth of the electrodeassembly 106 in the longitudinal direction such that any increase in theFeret diameter of the electrode assembly in the longitudinal directionover 1000 consecutive cycles of the secondary battery is less than 20%.By way of further example, in one embodiment the primary growthconstraint system 151 may be capable of restraining growth of theelectrode assembly 106 in the longitudinal direction such that anyincrease in the Feret diameter of the electrode assembly in thelongitudinal direction over 2000 consecutive cycles of the secondarybattery is less than 20%. By way of further example, in one embodimentthe primary growth constraint system 151 may be capable of restraininggrowth of the electrode assembly 106 in the longitudinal direction suchthat any increase in the Feret diameter of the electrode assembly in thelongitudinal direction over 3000 consecutive cycles of the secondarybattery to less than 20%. By way of further example, in one embodimentthe primary growth constraint system 151 may be capable of restraininggrowth of the electrode assembly 106 in the longitudinal direction suchthat any increase in the Feret diameter of the electrode assembly in thelongitudinal direction over 5000 consecutive cycles of the secondarybattery is less than 20%. By way of further example, in one embodimentthe primary growth constraint system 151 may be capable of restraininggrowth of the electrode assembly 106 in the longitudinal direction suchthat any increase in the Feret diameter of the electrode assembly in thelongitudinal direction over 8000 consecutive cycles of the secondarybattery is less than 20%. By way of further example, in one embodimentthe primary growth constraint system 151 may be capable of restraininggrowth of the electrode assembly 106 in the longitudinal direction suchthat any increase in the Feret diameter of the electrode assembly in thelongitudinal direction over 10,000 consecutive cycles of the secondarybattery is less than 20%.

In yet another embodiment, the set of electrode constraints 108including the primary growth constraint system 151 may be capable ofrestraining growth of the electrode assembly 106 in the longitudinaldirection such that any increase in the Feret diameter of the electrodeassembly in the longitudinal direction over 10 consecutive cycles of thesecondary battery is less than 10%. By way of further example, in oneembodiment the primary growth constraint system 151 may be capable ofrestraining growth of the electrode assembly 106 in the longitudinaldirection such that any increase in the Feret diameter of the electrodeassembly in the longitudinal direction over 20 consecutive cycles of thesecondary battery is less than 10%. By way of further example, in oneembodiment the primary growth constraint system 151 may be capable ofrestraining growth of the electrode assembly 106 in the longitudinaldirection such that any increase in the Feret diameter of the electrodeassembly in the longitudinal direction over 30 consecutive cycles of thesecondary battery is less than 10%. By way of further example, in oneembodiment the primary growth constraint system 151 may be capable ofrestraining growth of the electrode assembly 106 in the longitudinaldirection such that any increase in the Feret diameter of the electrodeassembly in the longitudinal direction over 50 consecutive cycles of thesecondary battery is less than 10%. By way of further example, in oneembodiment the primary growth constraint system 151 may be capable ofrestraining growth of the electrode assembly 106 in the longitudinaldirection such that any increase in the Feret diameter of the electrodeassembly in the longitudinal direction over 80 consecutive cycles of thesecondary battery is less than 10%. By way of further example, in oneembodiment the primary growth constraint system 151 may be capable ofrestraining growth of the electrode assembly 106 in the longitudinaldirection such that any increase in the Feret diameter of the electrodeassembly in the longitudinal direction over 100 consecutive cycles ofthe secondary battery is less than 10%. By way of further example, inone embodiment the primary growth constraint system 151 may be capableof restraining growth of the electrode assembly 106 in the longitudinaldirection such that any increase in the Feret diameter of the electrodeassembly in the longitudinal direction over 200 consecutive cycles ofthe secondary battery is less than 10%. By way of further example, inone embodiment the primary growth constraint system 151 may be capableof restraining growth of the electrode assembly 106 in the longitudinaldirection such that any increase in the Feret diameter of the electrodeassembly in the longitudinal direction over 300 consecutive cycles ofthe secondary battery is less than 10%. By way of further example, inone embodiment the primary growth constraint system 151 may be capableof restraining growth of the electrode assembly 106 in the longitudinaldirection such that any increase in the Feret diameter of the electrodeassembly in the longitudinal direction over 500 consecutive cycles ofthe secondary battery is less than 10%. By way of further example, inone embodiment the primary growth constraint system 151 may be capableof restraining growth of the electrode assembly 106 in the longitudinaldirection such that any increase in the Feret diameter of the electrodeassembly in the longitudinal direction such that any increase in theFeret diameter of the electrode assembly in the longitudinal directionover 800 consecutive cycles of the secondary battery is less than 10%between charged and discharged states. By way of further example, in oneembodiment the primary growth constraint system 151 may be capable ofrestraining growth of the electrode assembly 106 in the longitudinaldirection such that any increase in the Feret diameter of the electrodeassembly in the longitudinal direction over 1000 consecutive cycles ofthe secondary battery is less than 10%. By way of further example, inone embodiment the primary growth constraint system 151 may be capableof restraining growth of the electrode assembly 106 in the longitudinaldirection such that any increase in the Feret diameter of the electrodeassembly in the longitudinal direction over 2000 consecutive cycles isless than 10%. By way of further example, in one embodiment the primarygrowth constraint system 151 may be capable of restraining growth of theelectrode assembly 106 in the longitudinal direction such that anyincrease in the Feret diameter of the electrode assembly in thelongitudinal direction over 3000 consecutive cycles of the secondarybattery is less than 10%. By way of further example, in one embodimentthe primary growth constraint system 151 may be capable of restraininggrowth of the electrode assembly 106 in the longitudinal direction suchthat any increase in the Feret diameter of the electrode assembly in thelongitudinal direction over 5000 consecutive cycles of the secondarybattery is less than 10%. By way of further example, in one embodimentthe primary growth constraint system 151 may be capable of restraininggrowth of the electrode assembly 106 in the longitudinal direction suchthat any increase in the Feret diameter of the electrode assembly in thelongitudinal direction over 8000 consecutive cycles of the secondarybattery is less than 10%. By way of further example, in one embodimentthe primary growth constraint system 151 may be capable of restraininggrowth of the electrode assembly 106 in the longitudinal direction suchthat any increase in the Feret diameter of the electrode assembly in thelongitudinal direction over 10,000 consecutive cycles of the secondarybattery is less than 10%.

In yet another embodiment, the set of electrode constraints 108including the primary growth constraint system 151 may be capable ofrestraining growth of the electrode assembly 106 in the longitudinaldirection such that any increase in the Feret diameter of the electrodeassembly in the longitudinal direction over 5 consecutive cycles of thesecondary battery is less than 5%. By way of further example, in oneembodiment the primary growth constraint system 151 may be capable ofrestraining growth of the electrode assembly 106 in the longitudinaldirection such that any increase in the Feret diameter of the electrodeassembly in the longitudinal direction over 10 consecutive cycles of thesecondary battery is less than 5%. By way of further example, in oneembodiment the primary growth constraint system 151 may be capable ofrestraining growth of the electrode assembly 106 in the longitudinaldirection such that any increase in the Feret diameter of the electrodeassembly in the longitudinal direction over 20 consecutive cycles of thesecondary battery is less than 5%. By way of further example, in oneembodiment the primary growth constraint system 151 may be capable ofrestraining growth of the electrode assembly 106 in the longitudinaldirection such that any increase in the Feret diameter of the electrodeassembly in the longitudinal direction over 30 consecutive cycles of thesecondary battery is less than 5%. By way of further example, in oneembodiment the primary growth constraint system 151 may be capable ofrestraining growth of the electrode assembly 106 in the longitudinaldirection such that any increase in the Feret diameter of the electrodeassembly in the longitudinal direction over 50 consecutive cycles of thesecondary battery is less than 5%. By way of further example, in oneembodiment the primary growth constraint system 151 may be capable ofrestraining growth of the electrode assembly 106 in the longitudinaldirection such that any increase in the Feret diameter of the electrodeassembly in the longitudinal direction over 80 consecutive cycles of thesecondary battery is less than 5%. By way of further example, in oneembodiment the primary growth constraint system 151 may be capable ofrestraining growth of the electrode assembly 106 in the longitudinaldirection such that any increase in the Feret diameter of the electrodeassembly in the longitudinal direction over 100 consecutive cycles ofthe secondary battery, is less than 5. By way of further example, in oneembodiment the primary growth constraint system 151 may be capable ofrestraining growth of the electrode assembly 106 in the longitudinaldirection such that any increase in the Feret diameter of the electrodeassembly in the longitudinal direction over 200 consecutive cycles ofthe secondary battery is less than 5%. By way of further example, in oneembodiment the primary growth constraint system 151 may be capable ofrestraining growth of the electrode assembly 106 in the longitudinaldirection such that any increase in the Feret diameter of the electrodeassembly in the longitudinal direction over 300 consecutive cycles ofthe secondary battery is less than 5%. By way of further example, in oneembodiment the primary growth constraint system 151 may be capable ofrestraining growth of the electrode assembly 106 in the longitudinaldirection such that any increase in the Feret diameter of the electrodeassembly in the longitudinal direction over 500 consecutive cycles ofthe secondary battery is less than 5%. By way of further example, in oneembodiment the primary growth constraint system 151 may be capable ofrestraining growth of the electrode assembly 106 in the longitudinaldirection such that any increase in the Feret diameter of the electrodeassembly in the longitudinal direction over 800 consecutive cycles ofthe secondary battery is less than 5%. By way of further example, in oneembodiment the primary growth constraint system 151 may be capable ofrestraining growth of the electrode assembly 106 in the longitudinaldirection such that any increase in the Feret diameter of the electrodeassembly in the longitudinal direction over 1000 consecutive cycles ofthe secondary battery is less than 5% between charged and dischargedstates. By way of further example, in one embodiment the primary growthconstraint system 151 may be capable of restraining growth of theelectrode assembly 106 in the longitudinal direction such that anyincrease in the Feret diameter of the electrode assembly in thelongitudinal direction over 2000 consecutive cycles of the secondarybattery is less than 5% between charged and discharged states. By way offurther example, in one embodiment the primary growth constraint system151 may be capable of restraining growth of the electrode assembly 106in the longitudinal direction such that any increase in the Feretdiameter of the electrode assembly in the longitudinal direction over3000 consecutive cycles of the secondary battery is less than 5%. By wayof further example, in one embodiment the primary growth constraintsystem 151 may be capable of restraining growth of the electrodeassembly 106 in the longitudinal direction such that any increase in theFeret diameter of the electrode assembly in the longitudinal directionover 5000 consecutive cycles of the secondary battery is less than 5%.By way of further example, in one embodiment the primary growthconstraint system 151 may be capable of restraining growth of theelectrode assembly 106 in the longitudinal direction such that anyincrease in the Feret diameter of the electrode assembly in thelongitudinal direction over 8000 consecutive cycles of the secondarybattery is less than 5%. By way of further example, in one embodimentthe primary growth constraint system 151 may be capable of restraininggrowth of the electrode assembly 106 in the longitudinal direction suchthat any increase in the Feret diameter of the electrode assembly in thelongitudinal direction over 10,000 consecutive cycles of the secondarybattery is less than 5%.

In yet another embodiment, the set of electrode constraints 108including the primary growth constraint system 151 may be capable ofrestraining growth of the electrode assembly 106 in the longitudinaldirection such that any increase in the Feret diameter of the electrodeassembly in the longitudinal direction per cycle of the secondarybattery is less than 1%. By way of further example, in one embodimentthe primary growth constraint system 151 may be capable of restraininggrowth of the electrode assembly 106 in the longitudinal direction suchthat any increase in the Feret diameter of the electrode assembly in thelongitudinal direction over 5 consecutive cycles of the secondarybattery is less than 1%. By way of further example, in one embodimentthe primary growth constraint system 151 may be capable of restraininggrowth of the electrode assembly 106 in the longitudinal direction suchthat any increase in the Feret diameter of the electrode assembly in thelongitudinal direction over 10 consecutive cycles of the secondarybattery is less than 1%. By way of further example, in one embodimentthe primary growth constraint system 151 may be capable of restraininggrowth of the electrode assembly 106 in the longitudinal direction suchthat any increase in the Feret diameter of the electrode assembly in thelongitudinal direction over 20 consecutive cycles of the secondarybattery is less than 1%. By way of further example, in one embodimentthe primary growth constraint system 151 may be capable of restraininggrowth of the electrode assembly 106 in the longitudinal direction suchthat any increase in the Feret diameter of the electrode assembly in thelongitudinal direction over 30 consecutive cycles of the secondarybattery is less than 1%. By way of further example, in one embodimentthe primary growth constraint system 151 may be capable of restraininggrowth of the electrode assembly 106 in the longitudinal direction suchthat any increase in the Feret diameter of the electrode assembly in thelongitudinal direction over 50 consecutive cycles of the secondarybattery is less than 1%. By way of further example, in one embodimentthe primary growth constraint system 151 may be capable of restraininggrowth of the electrode assembly 106 in the longitudinal direction suchthat any increase in the Feret diameter of the electrode assembly in thelongitudinal direction over 80 consecutive cycles of the secondarybattery is less than 1%. By way of further example, in one embodimentthe primary growth constraint system 151 may be capable of restraininggrowth of the electrode assembly 106 in the longitudinal direction suchthat any increase in the Feret diameter of the electrode assembly in thelongitudinal direction over 100 consecutive cycles of the secondarybattery is less than 1%. By way of further example, in one embodimentthe primary growth constraint system 151 may be capable of restraininggrowth of the electrode assembly 106 in the longitudinal direction suchthat any increase in the Feret diameter of the electrode assembly in thelongitudinal direction over 200 consecutive cycles of the secondarybattery is less than 1%. By way of further example, in one embodimentthe primary growth constraint system 151 may be capable of restraininggrowth of the electrode assembly 106 in the longitudinal direction suchthat any increase in the Feret diameter of the electrode assembly in thelongitudinal direction over 300 consecutive cycles of the secondarybattery is less than 1%. By way of further example, in one embodimentthe primary growth constraint system 151 may be capable of restraininggrowth of the electrode assembly 106 in the longitudinal direction suchthat any increase in the Feret diameter of the electrode assembly in thelongitudinal direction over 500 consecutive cycles of the secondarybattery is less than 1%. By way of further example, in one embodimentthe primary growth constraint system 151 may be capable of restraininggrowth of the electrode assembly 106 in the longitudinal direction suchthat any increase in the Feret diameter of the electrode assembly in thelongitudinal direction over 800 consecutive cycles of the secondarybattery is less than 1%. By way of further example, in one embodimentthe primary growth constraint system 151 may be capable of restraininggrowth of the electrode assembly 106 in the longitudinal direction suchthat any increase in the Feret diameter of the electrode assembly in thelongitudinal direction over 1000 consecutive cycles of the secondarybattery is less than 1%. By way of further example, in one embodimentthe primary growth constraint system 151 may be capable of restraininggrowth of the electrode assembly 106 in the longitudinal direction suchthat any increase in the Feret diameter of the electrode assembly in thelongitudinal direction over 2000 consecutive cycles of the secondarybattery is less than 1%. By way of further example, in one embodimentthe primary growth constraint system 151 may be capable of restraininggrowth of the electrode assembly 106 in the longitudinal direction suchthat any increase in the Feret diameter of the electrode assembly in thelongitudinal direction over 3000 consecutive cycles of the secondarybattery is less than 1%. By way of further example, in one embodimentthe primary growth constraint system 151 may be capable of restraininggrowth of the electrode assembly 106 in the longitudinal direction suchthat any increase in the Feret diameter of the electrode assembly in thelongitudinal direction over 5000 consecutive cycles of the secondarybattery is less than 1% between charged and discharged states. By way offurther example, in one embodiment the primary growth constraint system151 may be capable of restraining growth of the electrode assembly 106in the longitudinal direction such that any increase in the Feretdiameter of the electrode assembly in the longitudinal direction over8000 consecutive cycles of the secondary battery to less than 1%. By wayof further example, in one embodiment the primary growth constraintsystem 151 may be capable of restraining growth of the electrodeassembly 106 in the longitudinal direction such that any increase in theFeret diameter of the electrode assembly in the longitudinal directionover 10,000 consecutive cycles of the secondary battery to less than 1%.

By charged state it is meant that the secondary battery 102 is chargedto at least 75% of its rated capacity, such as at least 80% of its ratedcapacity, and even at least 90% of its rated capacity, such as at least95% of its rated capacity, and even 100% of its rated capacity. Bydischarged state it is meant that the secondary battery is discharged toless than 25% of its rated capacity, such as less than 20% of its ratedcapacity, and even less than 10%, such as less than 5%, and even 0% ofits rated capacity. Furthermore, it is noted that the actual capacity ofthe secondary battery 102 may vary over time and with the number ofcycles the battery has gone through. That is, while the secondarybattery 102 may initially exhibit an actual measured capacity that isclose to its rated capacity, the actual capacity of the battery willdecrease over time, with the secondary battery 102 being considered tobe at the end of its life when the actual capacity drops below 80% ofthe rated capacity as measured in going from a charged to a dischargedstate.

Further shown in FIGS. 6A and 6B, the set of electrode constraints 108can further comprise the secondary growth constraint system 152, thatcan generally comprise first and second secondary growth constraints158, 160, respectively, that are separated from one another along asecond direction orthogonal to the longitudinal direction, such as alongthe vertical axis (Z axis) in the embodiment as shown. For example, inone embodiment, the first secondary growth constraint 158 at leastpartially extends across a first region 148 of the lateral surface 142of the electrode assembly 106, and the second secondary growthconstraint 160 at least partially extends across a second region 150 ofthe lateral surface 142 of the electrode assembly 106 that opposes thefirst region 148. In yet another version, one or more of the first andsecond secondary growth constraints 154, 156 may be interior to thelateral surface 142 of the electrode assembly 106, such as when one ormore of the secondary growth constraints comprise an internal structureof the electrode assembly 106. In one embodiment, the first and secondsecondary growth constraints 158, 160, respectively, are connected by atleast one secondary connecting member 166, which may have a principalaxis that is parallel to the second direction, such as the verticalaxis. The secondary connecting member 166 may serve to connect and holdthe first and second secondary growth constraints 158, 160,respectively, in tension with one another, so as to restrain growth ofthe electrode assembly 106 along a direction orthogonal to thelongitudinal direction, such as for example to restrain growth in thevertical direction (e.g., along the Z axis). In the embodiment depictedin FIG. 6A, the at least one secondary connecting member 166 cancorrespond to at least one of the first and second primary growthconstraints 154, 156. However, the secondary connecting member 166 isnot limited thereto, and can alternatively and/or in addition compriseother structures and/or configurations.

According to one embodiment, the set of constraints including thesecondary growth constraint system 152 may be capable of restraininggrowth of the electrode assembly 106 in a second direction orthogonal tothe longitudinal direction, such as the vertical direction (Z axis),such that any increase in the Feret diameter of the electrode assemblyin the second direction over 20 consecutive cycles of the secondarybattery is less than 20%. By way of further example, in one embodimentthe secondary growth constraint system 152 may be capable of restraininggrowth of the electrode assembly 106 in the second direction such thatany increase in the Feret diameter of the electrode assembly in thesecond direction over 30 consecutive cycles of the secondary battery isless than 20%. By way of further example, in one embodiment thesecondary growth constraint system 152 may be capable of restraininggrowth of the electrode assembly 106 in the second direction such thatany increase in the Feret diameter of the electrode assembly in thesecond direction over 50 consecutive cycles of the secondary battery isless than 20%. By way of further example, in one embodiment thesecondary growth constraint system 152 may be capable of restraininggrowth of the electrode assembly 106 in the second direction such thatany increase in the Feret diameter of the electrode assembly in thesecond direction over 80 consecutive cycles of the secondary battery isless than 20%. By way of further example, in one embodiment thesecondary growth constraint system 152 may be capable of restraininggrowth of the electrode assembly 106 in the second direction such thatany increase in the Feret diameter of the electrode assembly in thesecond direction over 100 consecutive cycles of the secondary battery isless than 20%. By way of further example, in one embodiment thesecondary growth constraint system 152 may be capable of restraininggrowth of the electrode assembly 106 in the second direction such thatany increase in the Feret diameter of the electrode assembly in thesecond direction over 200 consecutive cycles of the secondary battery isless than 20%. By way of further example, in one embodiment thesecondary growth constraint system 152 may be capable of restraininggrowth of the electrode assembly 106 in the second direction such thatany increase in the Feret diameter of the electrode assembly in thesecond direction over 300 consecutive cycles of the secondary battery isless than 20%. By way of further example, in one embodiment thesecondary growth constraint system 152 may be capable of restraininggrowth of the electrode assembly 106 in the second direction such thatany increase in the Feret diameter of the electrode assembly in thesecond direction over 500 consecutive cycles of the secondary battery isless than 20%. By way of further example, in one embodiment thesecondary growth constraint system 152 may be capable of restraininggrowth of the electrode assembly 106 in the second direction such thatany increase in the Feret diameter of the electrode assembly in thesecond direction over 800 consecutive cycles of the secondary battery isless than 20%. By way of further example, in one embodiment thesecondary growth constraint system 152 may be capable of restraininggrowth of the electrode assembly 106 in the second direction such thatany increase in the Feret diameter of the electrode assembly in thesecond direction over 1000 consecutive cycles of the secondary batteryis less than 20%. By way of further example, in one embodiment thesecondary growth constraint system 151 may be capable of restraininggrowth of the electrode assembly 106 in the second direction such thatany increase in the Feret diameter of the electrode assembly in thesecond direction over 2000 consecutive cycles of the secondary batteryis less than 20%. By way of further example, in one embodiment thesecondary growth constraint system 152 may be capable of restraininggrowth of the electrode assembly 106 in the second direction such thatany increase in the Feret diameter of the electrode assembly in thesecond direction over 3000 consecutive cycles of the secondary batteryis less than 20%. By way of further example, in one embodiment thesecondary growth constraint system 152 may be capable of restraininggrowth of the electrode assembly 106 in the second direction such thatany increase in the Feret diameter of the electrode assembly in thesecond direction over 5000 consecutive cycles of the secondary batteryis less than 20%. By way of further example, in one embodiment thesecondary growth constraint system 152 may be capable of restraininggrowth of the electrode assembly 106 in the second direction such thatany increase in the Feret diameter of the electrode assembly in thesecond direction over 8000 consecutive cycles of the secondary batteryis less than 20%. By way of further example, in one embodiment thesecondary growth constraint system 151 may be capable of restraininggrowth of the electrode assembly 106 in the second direction such thatany increase in the Feret diameter of the electrode assembly in thesecond direction over 10,000 consecutive cycles of the secondary batteryis less than 20% between charged and discharged states.

In embodiment, the set of constraints including the secondary growthconstraint system 152 may be capable of restraining growth of theelectrode assembly 106 in the second direction such that any increase inthe Feret diameter of the electrode assembly in the second directionover 10 consecutive cycles of the secondary battery is less than 10%between charged and discharged states. By way of further example, in oneembodiment the secondary growth constraint system 152 may be capable ofrestraining growth of the electrode assembly 106 in the second directionsuch that any increase in the Feret diameter of the electrode assemblyin the second direction over 20 consecutive cycles of the secondarybattery is less than 10%. By way of further example, in one embodimentthe secondary growth constraint system 152 may be capable of restraininggrowth of the electrode assembly 106 in the second direction such thatany increase in the Feret diameter of the electrode assembly in thesecond direction over 30 consecutive cycles of the secondary battery isless than 10%. By way of further example, in one embodiment thesecondary growth constraint system 152 may be capable of restraininggrowth of the electrode assembly 106 in the second direction such thatany increase in the Feret diameter of the electrode assembly in thesecond direction over 50 consecutive cycles of the secondary battery isless than 10%. By way of further example, in one embodiment thesecondary growth constraint system 152 may be capable of restraininggrowth of the electrode assembly 106 in the second direction such thatany increase in the Feret diameter of the electrode assembly in thesecond direction over 80 consecutive cycles of the secondary battery isless than 10%. By way of further example, in one embodiment thesecondary growth constraint system 152 may be capable of restraininggrowth of the electrode assembly 106 in the second direction such thatany increase in the Feret diameter of the electrode assembly in thesecond direction over 100 consecutive cycles of the secondary battery isless than 10%. By way of further example, in one embodiment thesecondary growth constraint system 152 may be capable of restraininggrowth of the electrode assembly 106 in the second direction such thatany increase in the Feret diameter of the electrode assembly in thesecond direction over 200 consecutive cycles of the secondary battery isless than 10%. By way of further example, in one embodiment thesecondary growth constraint system 152 may be capable of restraininggrowth of the electrode assembly 106 in the second direction such thatany increase in the Feret diameter of the electrode assembly in thesecond direction over 300 consecutive cycles of the secondary battery isless than 10%. By way of further example, in one embodiment thesecondary growth constraint system 152 may be capable of restraininggrowth of the electrode assembly 106 in the second direction such thatany increase in the Feret diameter of the electrode assembly in thesecond direction over 500 consecutive cycles of the secondary battery isless than 10%. By way of further example, in one embodiment thesecondary growth constraint system 152 may be capable of restraininggrowth of the electrode assembly 106 in the second direction such thatany increase in the Feret diameter of the electrode assembly in thesecond direction over 800 consecutive cycles of the secondary battery isless than 10%. By way of further example, in one embodiment thesecondary growth constraint system 152 may be capable of restraininggrowth of the electrode assembly 106 in the second direction such thatany increase in the Feret diameter of the electrode assembly in thesecond direction over 1000 consecutive cycles of the secondary batteryis less than 10%. By way of further example, in one embodiment thesecondary growth constraint system 151 may be capable of restraininggrowth of the electrode assembly 106 in the second direction such thatany increase in the Feret diameter of the electrode assembly in thesecond direction over 2000 consecutive cycles of the secondary batteryis less than 10%. By way of further example, in one embodiment thesecondary growth constraint system 152 may be capable of restraininggrowth of the electrode assembly 106 in the second direction such thatany increase in the Feret diameter of the electrode assembly in thesecond direction over 3000 consecutive cycles of the secondary batteryis less than 10%. By way of further example, in one embodiment thesecondary growth constraint system 152 may be capable of restraininggrowth of the electrode assembly 106 in the second direction such thatany increase in the Feret diameter of the electrode assembly in thesecond direction over 5000 consecutive cycles of the secondary batteryis less than 10%. By way of further example, in one embodiment thesecondary growth constraint system 152 may be capable of restraininggrowth of the electrode assembly 106 in the second direction such thatany increase in the Feret diameter of the electrode assembly in thesecond direction over 8000 consecutive cycles of the secondary batteryis less than 10%. By way of further example, in one embodiment thesecondary growth constraint system 151 may be capable of restraininggrowth of the electrode assembly 106 in the second direction such thatany increase in the Feret diameter of the electrode assembly in thesecond direction over 10,000 consecutive cycles of the secondary batteryis less than 10%.

In embodiment, the set of constraints including the secondary growthconstraint system 152 may be capable of restraining growth of theelectrode assembly 106 in the second direction such that any increase inthe Feret diameter of the electrode assembly in the second directionover 5 consecutive cycles of the secondary battery is less than 5%between charged and discharged states. By way of further example, in oneembodiment the secondary growth constraint system 152 may be capable ofrestraining growth of the electrode assembly 106 in the second directionsuch that any increase in the Feret diameter of the electrode assemblyin the second direction over 10 consecutive cycles of the secondarybattery is less than 5%. By way of further example, in one embodimentthe secondary growth constraint system 152 may be capable of restraininggrowth of the electrode assembly 106 in the second direction such thatany increase in the Feret diameter of the electrode assembly in thesecond direction over 20 consecutive cycles of the secondary battery isless than 5%. By way of further example, in one embodiment the secondarygrowth constraint system 152 may be capable of restraining growth of theelectrode assembly 106 in the second direction such that any increase inthe Feret diameter of the electrode assembly in the second directionover 30 consecutive cycles of the secondary battery is less than 5%. Byway of further example, in one embodiment the secondary growthconstraint system 152 may be capable of restraining growth of theelectrode assembly 106 in the second direction such that any increase inthe Feret diameter of the electrode assembly in the second directionover 50 consecutive cycles of the secondary battery is less than 5%. Byway of further example, in one embodiment the secondary growthconstraint system 152 may be capable of restraining growth of theelectrode assembly 106 in the second direction such that any increase inthe Feret diameter of the electrode assembly in the second directionover 80 consecutive cycles of the secondary battery is less than 5%. Byway of further example, in one embodiment the secondary growthconstraint system 152 may be capable of restraining growth of theelectrode assembly 106 in the second direction such that any increase inthe Feret diameter of the electrode assembly in the second directionover 100 consecutive cycles of the secondary battery is less than 5%. Byway of further example, in one embodiment the secondary growthconstraint system 152 may be capable of restraining growth of theelectrode assembly 106 in the second direction such that any increase inthe Feret diameter of the electrode assembly in the second directionover 200 consecutive cycles of the secondary battery is less than 5%. Byway of further example, in one embodiment the secondary growthconstraint system 152 may be capable of restraining growth of theelectrode assembly 106 in the second direction such that any increase inthe Feret diameter of the electrode assembly in the second directionover 300 consecutive cycles of the secondary battery is less than 5%. Byway of further example, in one embodiment the secondary growthconstraint system 152 may be capable of restraining growth of theelectrode assembly 106 in the second direction such that any increase inthe Feret diameter of the electrode assembly in the second directionover 500 consecutive cycles of the secondary battery is less than 5%. Byway of further example, in one embodiment the secondary growthconstraint system 152 may be capable of restraining growth of theelectrode assembly 106 in the second direction such that any increase inthe Feret diameter of the electrode assembly in the second directionover 800 consecutive cycles of the secondary battery is less than 5%. Byway of further example, in one embodiment the secondary growthconstraint system 152 may be capable of restraining growth of theelectrode assembly 106 in the second direction such that any increase inthe Feret diameter of the electrode assembly in the second directionover 1000 consecutive cycles of the secondary battery is less than 5%.By way of further example, in one embodiment the secondary growthconstraint system 151 may be capable of restraining growth of theelectrode assembly 106 in the second direction such that any increase inthe Feret diameter of the electrode assembly in the second directionover 2000 consecutive cycles of the secondary battery is less than 5%.By way of further example, in one embodiment the secondary growthconstraint system 152 may be capable of restraining growth of theelectrode assembly 106 in the second direction such that any increase inthe Feret diameter of the electrode assembly in the second directionover 3000 consecutive cycles of the secondary battery is less than 5%.By way of further example, in one embodiment the secondary growthconstraint system 152 may be capable of restraining growth of theelectrode assembly 106 in the second direction such that any increase inthe Feret diameter of the electrode assembly in the second directionover 5000 consecutive cycles of the secondary battery is less than 5%.By way of further example, in one embodiment the secondary growthconstraint system 152 may be capable of restraining growth of theelectrode assembly 106 in the second direction such that any increase inthe Feret diameter of the electrode assembly in the second directionover 8000 consecutive cycles of the secondary battery is less than 5%.By way of further example, in one embodiment the secondary growthconstraint system 151 may be capable of restraining growth of theelectrode assembly 106 in the second direction such that any increase inthe Feret diameter of the electrode assembly in the second directionover 10,000 consecutive cycles of the secondary battery is less than 5%.

In embodiment, the set of constraints including the secondary growthconstraint system 152 may be capable of restraining growth of theelectrode assembly 106 in the second direction such that any increase inthe Feret diameter of the electrode assembly in the second direction percycle of the secondary battery is less than 1%. By way of furtherexample, in one embodiment the secondary growth constraint system 152may be capable of restraining growth of the electrode assembly 106 inthe second direction such that any increase in the Feret diameter of theelectrode assembly in the second direction over 5 consecutive cycles ofthe secondary battery is less than 1%. By way of further example, in oneembodiment the secondary growth constraint system 152 may be capable ofrestraining growth of the electrode assembly 106 in the second directionsuch that any increase in the Feret diameter of the electrode assemblyin the second direction over 10 consecutive cycles of the secondarybattery is less than 1%. By way of further example, in one embodimentthe secondary growth constraint system 152 may be capable of restraininggrowth of the electrode assembly 106 in the second direction such thatany increase in the Feret diameter of the electrode assembly in thesecond direction over 20 consecutive cycles of the secondary battery isless than 1%. By way of further example, in one embodiment the secondarygrowth constraint system 152 may be capable of restraining growth of theelectrode assembly 106 in the second direction such that any increase inthe Feret diameter of the electrode assembly in the second directionover 30 consecutive cycles of the secondary battery is less than 1%. Byway of further example, in one embodiment the secondary growthconstraint system 152 may be capable of restraining growth of theelectrode assembly 106 in the second direction such that any increase inthe Feret diameter of the electrode assembly in the second directionover 50 consecutive cycles of the secondary battery is less than 1%. Byway of further example, in one embodiment the secondary growthconstraint system 152 may be capable of restraining growth of theelectrode assembly 106 in the second direction such that any increase inthe Feret diameter of the electrode assembly in the second directionover 80 consecutive cycles of the secondary battery is less than 1%. Byway of further example, in one embodiment the secondary growthconstraint system 152 may be capable of restraining growth of theelectrode assembly 106 in the second direction such that any increase inthe Feret diameter of the electrode assembly in the second directionover 100 consecutive cycles of the secondary battery is less than 1%. Byway of further example, in one embodiment the secondary growthconstraint system 152 may be capable of restraining growth of theelectrode assembly 106 in the second direction such that any increase inthe Feret diameter of the electrode assembly in the second directionover 200 consecutive cycles of the secondary battery is less than 1%. Byway of further example, in one embodiment the secondary growthconstraint system 152 may be capable of restraining growth of theelectrode assembly 106 in the second direction such that any increase inthe Feret diameter of the electrode assembly in the second directionover 300 consecutive cycles of the secondary battery is less than 1%. Byway of further example, in one embodiment the secondary growthconstraint system 152 may be capable of restraining growth of theelectrode assembly 106 in the second direction such that any increase inthe Feret diameter of the electrode assembly in the second directionover 500 consecutive cycles of the secondary battery is less than 1%. Byway of further example, in one embodiment the secondary growthconstraint system 152 may be capable of restraining growth of theelectrode assembly 106 in the second direction such that any increase inthe Feret diameter of the electrode assembly in the second directionover 800 consecutive cycles of the secondary battery is less than 1%. Byway of further example, in one embodiment the secondary growthconstraint system 152 may be capable of restraining growth of theelectrode assembly 106 in the second direction such that any increase inthe Feret diameter of the electrode assembly in the second directionover 1000 consecutive cycles of the secondary battery is less than 1%.By way of further example, in one embodiment the secondary growthconstraint system 151 may be capable of restraining growth of theelectrode assembly 106 in the second direction such that any increase inthe Feret diameter of the electrode assembly in the second directionover 2000 consecutive cycles of the secondary battery is less than 1%.By way of further example, in one embodiment the secondary growthconstraint system 152 may be capable of restraining growth of theelectrode assembly 106 in the second direction such that any increase inthe Feret diameter of the electrode assembly in the second directionover 3000 consecutive cycles of the secondary battery is less than 1%between charged and discharged states. By way of further example, in oneembodiment the secondary growth constraint system 152 may be capable ofrestraining growth of the electrode assembly 106 in the second directionsuch that any increase in the Feret diameter of the electrode assemblyin the second direction over 5000 consecutive cycles of the secondarybattery is less than 1%. By way of further example, in one embodimentthe secondary growth constraint system 152 may be capable of restraininggrowth of the electrode assembly 106 in the second direction such thatany increase in the Feret diameter of the electrode assembly in thesecond direction over 8000 consecutive cycles of the secondary batteryis less than 1%. By way of further example, in one embodiment thesecondary growth constraint system 151 may be capable of restraininggrowth of the electrode assembly 106 in the second direction such thatany increase in the Feret diameter of the electrode assembly in thesecond direction over 10,000 consecutive cycles of the secondary batteryis less than 1%.

FIG. 6C shows an embodiment of a set of electrode constraints 108 thatfurther includes a tertiary growth constraint system 155 to constraingrowth of the electrode assembly in a third direction that is orthogonalto the longitudinal and second directions, such as the transversedirection (X) direction. The tertiary growth constraint system 155 canbe provided in addition to the primary and secondary growth constraintsystems 151, 152, respectively, to constrain overall growth of theelectrode assembly 106 in three dimensions, and/or may be provided incombination with one of the primary or secondary growth constraintsystems 151, 152, respectively, to constrain overall growth of theelectrode assembly 106 in two dimensions. FIG. 6C shows a cross-sectionof the electrode assembly 106 in FIG. 1A taken along the transverse axis(X axis), such that the resulting 2-D cross-section is illustrated withthe vertical axis (Z axis) and transverse axis (X axis). As shown inFIG. 6C, the tertiary growth constraint system 155 can generallycomprise first and second tertiary growth constraints 157, 159,respectively, that are separated from one another along the thirddirection such as the transverse direction (X axis). For example, in oneembodiment, the first tertiary growth constraint 157 at least partiallyextends across a first region 144 of the lateral surface 142 of theelectrode assembly 106, and the second tertiary growth constraint 159 atleast partially extends across a second region 146 of the lateralsurface 142 of the electrode assembly 106 that opposes the first region144 in the transverse direction. In yet another version, one or more ofthe first and second tertiary growth constraints 157, 159 may beinterior to the lateral surface 142 of the electrode assembly 106, suchas when one or more of the tertiary growth constraints comprise aninternal structure of the electrode assembly 106. In one embodiment, thefirst and second tertiary growth constraints 157, 159, respectively, areconnected by at least one tertiary connecting member 165, which may havea principal axis that is parallel to the third direction. The tertiaryconnecting member 165 may serve to connect and hold the first and secondtertiary growth constraints 157, 159, respectively, in tension with oneanother, so as to restrain growth of the electrode assembly 106 along adirection orthogonal to the longitudinal direction, for example, torestrain growth in the transverse direction (e.g., along the X axis). Inthe embodiment depicted in FIG. 6C, the at least one tertiary connectingmember 165 can correspond to at least one of the first and secondsecondary growth constraints 158, 160. However, the tertiary connectingmember 165 is not limited thereto, and can alternatively and/or inaddition comprise other structures and/or configurations. For example,the at least one tertiary connecting member 165 can, in one embodiment,correspond to at least one of the first and second primary growthconstraints 154, 156 (not shown).

According to one embodiment, the set of constraints having the tertiarygrowth constraint system 155 may be capable of restraining growth of theelectrode assembly 106 in a third direction orthogonal to thelongitudinal direction, such as the transverse direction (X axis), suchthat any increase in the Feret diameter of the electrode assembly in thethird direction over 20 consecutive cycles of the secondary battery isless than 20%. By way of further example, in one embodiment the tertiarygrowth constraint system 155 may be capable of restraining growth of theelectrode assembly 106 in the third direction such that any increase inthe Feret diameter of the electrode assembly in the third direction over30 consecutive cycles of the secondary battery is less than 20%. By wayof further example, in one embodiment the tertiary growth constraintsystem 155 may be capable of restraining growth of the electrodeassembly 106 in the third direction such that any increase in the Feretdiameter of the electrode assembly in the third direction over 50consecutive cycles of the secondary battery is less than 20%. By way offurther example, in one embodiment the tertiary growth constraint system155 may be capable of restraining growth of the electrode assembly 106in the third direction such that any increase in the Feret diameter ofthe electrode assembly in the third direction over 80 consecutive cyclesof the secondary battery is less than 20%. By way of further example, inone embodiment the tertiary growth constraint system 155 may be capableof restraining growth of the electrode assembly 106 in the thirddirection such that any increase in the Feret diameter of the electrodeassembly in the third direction over 100 consecutive cycles of thesecondary battery is less than 20%. By way of further example, in oneembodiment the tertiary growth constraint system 155 may be capable ofrestraining growth of the electrode assembly 106 in the third directionsuch that any increase in the Feret diameter of the electrode assemblyin the third direction over 200 consecutive cycles of the secondarybattery is less than 20%. By way of further example, in one embodimentthe tertiary growth constraint system 155 may be capable of restraininggrowth of the electrode assembly 106 in the third direction such thatany increase in the Feret diameter of the electrode assembly in thethird direction over 300 consecutive cycles of the secondary battery isless than 20%. By way of further example, in one embodiment the tertiarygrowth constraint system 155 may be capable of restraining growth of theelectrode assembly 106 in the third direction such that any increase inthe Feret diameter of the electrode assembly in the third direction over500 consecutive cycles of the secondary battery is less than 20%. By wayof further example, in one embodiment the tertiary growth constraintsystem 152 may be capable of restraining growth of the electrodeassembly 106 in the third direction such that any increase in the Feretdiameter of the electrode assembly in the third direction over 800consecutive cycles of the secondary battery is less than 20%. By way offurther example, in one embodiment the tertiary growth constraint system155 may be capable of restraining growth of the electrode assembly 106in the third direction such that any increase in the Feret diameter ofthe electrode assembly in the third direction over 1000 consecutivecycles of the secondary battery is less than 20%. By way of furtherexample, in one embodiment the tertiary growth constraint system 155 maybe capable of restraining growth of the electrode assembly 106 in thethird direction such that any increase in the Feret diameter of theelectrode assembly in the third direction over 2000 consecutive cyclesof the secondary battery is less than 20%. By way of further example, inone embodiment the tertiary growth constraint system 155 may be capableof restraining growth of the electrode assembly 106 in the thirddirection such that any increase in the Feret diameter of the electrodeassembly in the third direction over 3000 consecutive cycles of thesecondary battery is less than 20%. By way of further example, in oneembodiment the tertiary growth constraint system 155 may be capable ofrestraining growth of the electrode assembly 106 in the third directionsuch that any increase in the Feret diameter of the electrode assemblyin the third direction over 5000 consecutive cycles of the secondarybattery is less than 20%. By way of further example, in one embodimentthe tertiary growth constraint system 155 may be capable of restraininggrowth of the electrode assembly 106 in the third direction such thatany increase in the Feret diameter of the electrode assembly in thethird direction over 8000 consecutive cycles of the secondary battery isless than 20%. By way of further example, in one embodiment the tertiarygrowth constraint system 155 may be capable of restraining growth of theelectrode assembly 106 in the third direction such that any increase inthe Feret diameter of the electrode assembly in the third direction over10,000 consecutive cycles of the secondary battery is less than 20%.

In one embodiment, the set of constraints having the tertiary growthconstraint system 155 may be capable of restraining growth of theelectrode assembly 106 in the third direction such that any increase inthe Feret diameter of the electrode assembly in the third direction over10 consecutive cycles of the secondary battery is less than 10%. By wayof further example, in one embodiment the tertiary growth constraintsystem 155 may be capable of restraining growth of the electrodeassembly 106 in the third direction such that any increase in the Feretdiameter of the electrode assembly in the third direction over 20consecutive cycles of the secondary battery is less than 10%. By way offurther example, in one embodiment the tertiary growth constraint system155 may be capable of restraining growth of the electrode assembly 106in the third direction such that any increase in the Feret diameter ofthe electrode assembly in the third direction over 30 consecutive cyclesof the secondary battery is less than 10%. By way of further example, inone embodiment the tertiary growth constraint system 155 may be capableof restraining growth of the electrode assembly 106 in the thirddirection such that any increase in the Feret diameter of the electrodeassembly in the third direction over 50 consecutive cycles of thesecondary battery is less than 10%. By way of further example, in oneembodiment the tertiary growth constraint system 155 may be capable ofrestraining growth of the electrode assembly 106 in the third directionsuch that any increase in the Feret diameter of the electrode assemblyin the third direction over 80 consecutive cycles of the secondarybattery is less than 10%. By way of further example, in one embodimentthe tertiary growth constraint system 155 may be capable of restraininggrowth of the electrode assembly 106 in the third direction such thatany increase in the Feret diameter of the electrode assembly in thethird direction over 100 consecutive cycles of the secondary battery isless than 10%. By way of further example, in one embodiment the tertiarygrowth constraint system 155 may be capable of restraining growth of theelectrode assembly 106 in the third direction such that any increase inthe Feret diameter of the electrode assembly in the third direction over200 consecutive cycles of the secondary battery is less than 10%. By wayof further example, in one embodiment the tertiary growth constraintsystem 155 may be capable of restraining growth of the electrodeassembly 106 in the third direction such that any increase in the Feretdiameter of the electrode assembly in the third direction over 300consecutive cycles of the secondary battery is less than 10%. By way offurther example, in one embodiment the tertiary growth constraint system155 may be capable of restraining growth of the electrode assembly 106in the third direction such that any increase in the Feret diameter ofthe electrode assembly in the third direction over 500 consecutivecycles of the secondary battery is less than 10%. By way of furtherexample, in one embodiment the tertiary growth constraint system 152 maybe capable of restraining growth of the electrode assembly 106 in thethird direction such that any increase in the Feret diameter of theelectrode assembly in the third direction over 800 consecutive cycles ofthe secondary battery is less than 10%. By way of further example, inone embodiment the tertiary growth constraint system 155 may be capableof restraining growth of the electrode assembly 106 in the thirddirection such that any increase in the Feret diameter of the electrodeassembly in the third direction over 1000 consecutive cycles of thesecondary battery is less than 10%. By way of further example, in oneembodiment the tertiary growth constraint system 155 may be capable ofrestraining growth of the electrode assembly 106 in the third directionsuch that any increase in the Feret diameter of the electrode assemblyin the third direction over 2000 consecutive cycles of the secondarybattery is less than 10%. By way of further example, in one embodimentthe tertiary growth constraint system 155 may be capable of restraininggrowth of the electrode assembly 106 in the third direction such thatany increase in the Feret diameter of the electrode assembly in thethird direction over 3000 consecutive cycles of the secondary battery isless than 10%. By way of further example, in one embodiment the tertiarygrowth constraint system 155 may be capable of restraining growth of theelectrode assembly 106 in the third direction such that any increase inthe Feret diameter of the electrode assembly in the third direction over5000 consecutive cycles of the secondary battery is less than 10%between charged and discharged states. By way of further example, in oneembodiment the tertiary growth constraint system 155 may be capable ofrestraining growth of the electrode assembly 106 in the third directionsuch that any increase in the Feret diameter of the electrode assemblyin the third direction over 8000 consecutive cycles of the secondarybattery is less than 10%. By way of further example, in one embodimentthe tertiary growth constraint system 155 may be capable of restraininggrowth of the electrode assembly 106 in the third direction such thatany increase in the Feret diameter of the electrode assembly in thethird direction over 10,000 consecutive cycles of the secondary batteryis less than 10%.

In one embodiment, the set of constraints having the tertiary growthconstraint system 155 may be capable of restraining growth of theelectrode assembly 106 in the third direction such that any increase inthe Feret diameter of the electrode assembly in the third direction over5 consecutive cycles of the secondary battery is less than 5%. By way offurther example, in one embodiment the tertiary growth constraint system155 may be capable of restraining growth of the electrode assembly 106in the third direction such that any increase in the Feret diameter ofthe electrode assembly in the third direction over 10 consecutive cyclesof the secondary battery is less than 5%. By way of further example, inone embodiment the tertiary growth constraint system 155 may be capableof restraining growth of the electrode assembly 106 in the thirddirection such that any increase in the Feret diameter of the electrodeassembly in the third direction over 20 consecutive cycles of thesecondary battery is less than 5%. By way of further example, in oneembodiment the tertiary growth constraint system 155 may be capable ofrestraining growth of the electrode assembly 106 in the third directionsuch that any increase in the Feret diameter of the electrode assemblyin the third direction over 30 consecutive cycles of the secondarybattery is less than 5%. By way of further example, in one embodimentthe tertiary growth constraint system 155 may be capable of restraininggrowth of the electrode assembly 106 in the third direction such thatany increase in the Feret diameter of the electrode assembly in thethird direction over 50 consecutive cycles of the secondary battery isless than 5%. By way of further example, in one embodiment the tertiarygrowth constraint system 155 may be capable of restraining growth of theelectrode assembly 106 in the third direction such that any increase inthe Feret diameter of the electrode assembly in the third direction over80 consecutive cycles of the secondary battery is less than 5%. By wayof further example, in one embodiment the tertiary growth constraintsystem 155 may be capable of restraining growth of the electrodeassembly 106 in the third direction such that any increase in the Feretdiameter of the electrode assembly in the third direction over 100consecutive cycles of the secondary battery is less than 5%. By way offurther example, in one embodiment the tertiary growth constraint system155 may be capable of restraining growth of the electrode assembly 106in the third direction such that any increase in the Feret diameter ofthe electrode assembly in the third direction over 200 consecutivecycles of the secondary battery is less than 5%. By way of furtherexample, in one embodiment the tertiary growth constraint system 155 maybe capable of restraining growth of the electrode assembly 106 in thethird direction such that any increase in the Feret diameter of theelectrode assembly in the third direction over 300 consecutive cycles ofthe secondary battery is less than 5%. By way of further example, in oneembodiment the tertiary growth constraint system 155 may be capable ofrestraining growth of the electrode assembly 106 in the third directionsuch that any increase in the Feret diameter of the electrode assemblyin the third direction over 500 consecutive cycles of the secondarybattery is less than 5%. By way of further example, in one embodimentthe tertiary growth constraint system 152 may be capable of restraininggrowth of the electrode assembly 106 in the third direction such thatany increase in the Feret diameter of the electrode assembly in thethird direction over 800 consecutive cycles of the secondary battery isless than 5%. By way of further example, in one embodiment the tertiarygrowth constraint system 155 may be capable of restraining growth of theelectrode assembly 106 in the third direction such that any increase inthe Feret diameter of the electrode assembly in the third direction over1000 consecutive cycles of the secondary battery is less than 5%. By wayof further example, in one embodiment the tertiary growth constraintsystem 155 may be capable of restraining growth of the electrodeassembly 106 in the third direction such that any increase in the Feretdiameter of the electrode assembly in the third direction over 2000consecutive cycles of the secondary battery is less than 5%. By way offurther example, in one embodiment the tertiary growth constraint system155 may be capable of restraining growth of the electrode assembly 106in the third direction such that any increase in the Feret diameter ofthe electrode assembly in the third direction over 3000 consecutivecycles of the secondary battery is less than 5%. By way of furtherexample, in one embodiment the tertiary growth constraint system 155 maybe capable of restraining growth of the electrode assembly 106 in thethird direction such that any increase in the Feret diameter of theelectrode assembly in the third direction over 5000 consecutive cyclesof the secondary battery is less than 5%. By way of further example, inone embodiment the tertiary growth constraint system 155 may be capableof restraining growth of the electrode assembly 106 in the thirddirection such that any increase in the Feret diameter of the electrodeassembly in the third direction over 8000 consecutive cycles of thesecondary battery is less than 5%. By way of further example, in oneembodiment the tertiary growth constraint system 155 may be capable ofrestraining growth of the electrode assembly 106 in the third directionsuch that any increase in the Feret diameter of the electrode assemblyin the third direction over 10,000 consecutive cycles of the secondarybattery is less than 5%.

In one embodiment, the set of constraints having the tertiary growthconstraint system 155 may be capable of restraining growth of theelectrode assembly 106 in the third direction such that any increase inthe Feret diameter of the electrode assembly in the third direction percycle of the secondary battery is less than 1%. By way of furtherexample, in one embodiment the tertiary growth constraint system 155 maybe capable of restraining growth of the electrode assembly 106 in thethird direction such that any increase in the Feret diameter of theelectrode assembly in the third direction over 5 consecutive cycles ofthe secondary battery is less than 1%. By way of further example, in oneembodiment the tertiary growth constraint system 155 may be capable ofrestraining growth of the electrode assembly 106 in the third directionsuch that any increase in the Feret diameter of the electrode assemblyin the third direction over 10 consecutive cycles of the secondarybattery is less than 1%. By way of further example, in one embodimentthe tertiary growth constraint system 155 may be capable of restraininggrowth of the electrode assembly 106 in the third direction such thatany increase in the Feret diameter of the electrode assembly in thethird direction over 20 consecutive cycles of the secondary battery isless than 1%. By way of further example, in one embodiment the tertiarygrowth constraint system 155 may be capable of restraining growth of theelectrode assembly 106 in the third direction such that any increase inthe Feret diameter of the electrode assembly in the third direction over30 consecutive cycles of the secondary battery is less than 1%. By wayof further example, in one embodiment the tertiary growth constraintsystem 155 may be capable of restraining growth of the electrodeassembly 106 in the third direction such that any increase in the Feretdiameter of the electrode assembly in the third direction over 50consecutive cycles of the secondary battery is less than 5%. By way offurther example, in one embodiment the tertiary growth constraint system155 may be capable of restraining growth of the electrode assembly 106in the third direction such that any increase in the Feret diameter ofthe electrode assembly in the third direction over 80 consecutive cyclesof the secondary battery is less than 1%. By way of further example, inone embodiment the tertiary growth constraint system 155 may be capableof restraining growth of the electrode assembly 106 in the thirddirection such that any increase in the Feret diameter of the electrodeassembly in the third direction over 100 consecutive cycles of thesecondary battery is less than 1%. By way of further example, in oneembodiment the tertiary growth constraint system 155 may be capable ofrestraining growth of the electrode assembly 106 in the third directionsuch that any increase in the Feret diameter of the electrode assemblyin the third direction over 200 consecutive cycles of the secondarybattery is less than 1%. By way of further example, in one embodimentthe tertiary growth constraint system 155 may be capable of restraininggrowth of the electrode assembly 106 in the third direction such thatany increase in the Feret diameter of the electrode assembly in thethird direction over 300 consecutive cycles of the secondary battery isless than 1%. By way of further example, in one embodiment the tertiarygrowth constraint system 155 may be capable of restraining growth of theelectrode assembly 106 in the third direction such that any increase inthe Feret diameter of the electrode assembly in the third direction over500 consecutive cycles of the secondary battery is less than 1%. By wayof further example, in one embodiment the tertiary growth constraintsystem 152 may be capable of restraining growth of the electrodeassembly 106 in the third direction such that any increase in the Feretdiameter of the electrode assembly in the third direction over 800consecutive cycles of the secondary battery is less than 1%. By way offurther example, in one embodiment the tertiary growth constraint system155 may be capable of restraining growth of the electrode assembly 106in the third direction such that any increase in the Feret diameter ofthe electrode assembly in the third direction over 1000 consecutivecycles of the secondary battery is less than 1% between charged anddischarged states. By way of further example, in one embodiment thetertiary growth constraint system 155 may be capable of restraininggrowth of the electrode assembly 106 in the third direction such thatany increase in the Feret diameter of the electrode assembly in thethird direction over 2000 consecutive cycles of the secondary battery isless than 1%. By way of further example, in one embodiment the tertiarygrowth constraint system 155 may be capable of restraining growth of theelectrode assembly 106 in the third direction such that any increase inthe Feret diameter of the electrode assembly in the third direction over3000 consecutive cycles of the secondary battery is less than 1%. By wayof further example, in one embodiment the tertiary growth constraintsystem 155 may be capable of restraining growth of the electrodeassembly 106 in the third direction such that any increase in the Feretdiameter of the electrode assembly in the third direction over 5000consecutive cycles of the secondary battery is less than 1%. By way offurther example, in one embodiment the tertiary growth constraint system155 may be capable of restraining growth of the electrode assembly 106in the third direction such that any increase in the Feret diameter ofthe electrode assembly in the third direction over 8000 consecutivecycles of the secondary battery is less than 1%. By way of furtherexample, in one embodiment the tertiary growth constraint system 155 maybe capable of restraining growth of the electrode assembly 106 in thethird direction such that any increase in the Feret diameter of theelectrode assembly in the third direction over 10,000 consecutive cyclesof the secondary battery is less than 1%.

According to one embodiment, the primary and secondary growth constraintsystems 151, 152, respectively, and optionally the tertiary growthconstraint system 155, are configured to cooperatively operate such thatportions of the primary growth constraint system 151 cooperatively actas a part of the secondary growth constraint system 152, and/or portionsof the secondary growth constraint system 152 cooperatively act as apart of the primary growth constraint system 151, and the portions ofany of the primary and/or secondary constraint systems 151, 152,respectively, may also cooperatively act as a part of the tertiarygrowth constraint system, and vice versa. For example, in the embodimentshown in in FIGS. 6A and 6B, the first and second primary connectingmembers 162, 164, respectively, of the primary growth constraint system151 can serve as at least a portion of, or even the entire structure of,the first and second secondary growth constraints 158, 160 thatconstrain growth in the second direction orthogonal to the longitudinaldirection. In yet another embodiment, as mentioned above, one or more ofthe first and second primary growth constraints 154, 156, respectively,can serve as one or more secondary connecting members 166 to connect thefirst and second secondary growth constrains 158, 160, respectively.Conversely, at least a portion of the first and second secondary growthconstraints 158, 160, respectively, can act as first and second primaryconnecting members 162, 164, respectively, of the primary growthconstraint system 151, and the at least one secondary connecting member166 of the secondary growth constraint system 152 can, in oneembodiment, act as one or more of the first and second primary growthconstraints 154, 156, respectively. In yet another embodiment, at leasta portion of the first and second primary connecting members 162, 164,respectively, of the primary growth constraint system 151, and/or the atleast one secondary connecting member 166 of the secondary growthconstraint system 152 can serve as at least a portion of, or even theentire structure of, the first and second tertiary growth constraints157, 159, respectively, that constrain growth in the transversedirection orthogonal to the longitudinal direction. In yet anotherembodiment, one or more of the first and second primary growthconstraints 154, 156, respectively, and/or the first and secondsecondary growth constraints 158, 160, respectively, can serve as one ormore tertiary connecting members 166 to connect the first and secondtertiary growth constraints 157, 159, respectively. Conversely, at leasta portion of the first and second tertiary growth constraints 157, 159,respectively, can act as first and second primary connecting members162, 164, respectively, of the primary growth constraint system 151,and/or the at least one secondary connecting member 166 of the secondarygrowth constraint system 152, and the at least one tertiary connectingmember 165 of the tertiary growth constraint system 155 can in oneembodiment act as one or more of the first and second primary growthconstraints 154, 156, respectively, and/or one or more of the first andsecond secondary growth constraints 158, 160, respectively.Alternatively and/or additionally, the primary and/or secondary and/ortertiary growth constraints can comprise other structures that cooperateto restrain growth of the electrode assembly 106. Accordingly, theprimary and secondary growth constraint systems 151, 152, respectively,and optionally the tertiary growth constraint system 155, can sharecomponents and/or structures to exert restraint on the growth of theelectrode assembly 106.

In one embodiment, the set of electrode constraints 108 can comprisestructures such as the primary and secondary growth constraints, andprimary and secondary connecting members, that are structures that areexternal to and/or internal to the battery enclosure 104, or may be apart of the battery enclosure 104 itself. For example, the set ofelectrode constraints 108 can comprise a combination of structures thatincludes the battery enclosure 104 as well as other structuralcomponents. In one such embodiment, the battery enclosure 104 may be acomponent of the primary growth constraint system 151 and/or thesecondary growth constraint system 152; stated differently, in oneembodiment, the battery enclosure 104, alone or in combination with oneor more other structures (within and/or outside the battery enclosure104, for example, the primary growth constraint system 151 and/or asecondary growth constraint system 152) restrains growth of theelectrode assembly 106 in the electrode stacking direction D and/or inthe second direction orthogonal to the stacking direction, D. Forexample, one or more of the primary growth constraints 154, 156 andsecondary growth constraints 158, 160 can comprise a structure that isinternal to the electrode assembly. In another embodiment, the primarygrowth constraint system 151 and/or secondary growth constraint system152 does not include the battery enclosure 104, and instead one or morediscrete structures (within and/or outside the battery enclosure 104)other than the battery enclosure 104 restrains growth of the electrodeassembly 106 in the electrode stacking direction, D, and/or in thesecond direction orthogonal to the stacking direction, D. The electrodeassembly 106 may be restrained by the set of electrode constraints 108at a pressure that is greater than the pressure exerted by growth and/orswelling of the electrode assembly 106 during repeated cycling of anenergy storage device 100 or a secondary battery having the electrodeassembly 106.

In one exemplary embodiment, the primary growth constraint system 151includes one or more discrete structure(s) within the battery enclosure104 that restrains growth of the anode structure 110 in the stackingdirection D by exerting a pressure that exceeds the pressure generatedby the anode structure 110 in the stacking direction D upon repeatedcycling of a secondary battery 102 having the anode structure 110 as apart of the electrode assembly 106. In another exemplary embodiment, theprimary growth constraint system 151 includes one or more discretestructures within the battery enclosure 104 that restrains growth of thecathode structure 112 in the stacking direction D by exerting a pressurein the stacking direction D that exceeds the pressure generated by theanode structure 112 in the stacking direction D upon repeated cycling ofa secondary battery 102 having the cathode structure 112 as a part ofthe electrode assembly 106. The secondary growth constraint system 152can similarly include one or more discrete structures within the batteryenclosure 104 that restrain growth of at least one of the anodestructures 110 and cathode structures 112 in the second directionorthogonal to the stacking direction D, such as along the vertical axis(Z axis), by exerting a pressure in the second direction that exceedsthe pressure generated by the anode or cathode structure 110, 112,respectively, in the second direction upon repeated cycling of asecondary battery 102 having the anode or cathode structures 110, 112,respectively.

In yet another embodiment, the first and second primary growthconstraints 154, 156, respectively, of the primary growth constraintsystem 151 restrain growth of the electrode assembly 106 by exerting apressure on the first and second longitudinal end surfaces 116, 118 ofthe electrode assembly 106, meaning, in a longitudinal direction, thatexceeds a pressure exerted by the first and second primary growthconstraints 154, 156 on other surfaces of the electrode assembly 106that would be in a direction orthogonal to the longitudinal direction,such as opposing first and second regions of the lateral surface 142 ofthe electrode assembly 106 along the transverse axis and/or verticalaxis. That is, the first and second primary growth constraints 154, 156may exert a pressure in a longitudinal direction (Y axis) that exceeds apressure generated thereby in directions orthogonal thereto, such as thetransverse (X axis) and vertical (Z axis) directions. For example, inone such embodiment, the primary growth constraint system 151 restrainsgrowth of the electrode assembly 106 with a pressure on first and secondlongitudinal end surfaces 116, 118 (i.e., in the stacking direction D)that exceeds the pressure maintained on the electrode assembly 106 bythe primary growth constraint system 151 in at least one, or even both,of the two directions that are perpendicular to the stacking directionD, by a factor of at least 3. By way of further example, in one suchembodiment, the primary growth constraint system 151 restrains growth ofthe electrode assembly 106 with a pressure on first and secondlongitudinal end surfaces 116, 118 (i.e., in the stacking direction D)that exceeds the pressure maintained on the electrode assembly 106 bythe primary growth constraint system 151 in at least one, or even both,of the two directions that are perpendicular to the stacking direction Dby a factor of at least 4. By way of further example, in one suchembodiment, the primary growth constraint system 151 restrains growth ofthe electrode assembly 106 with a pressure on first and secondlongitudinal end surfaces 116, 118 (i.e., in the stacking direction D)that exceeds the pressure maintained on the electrode assembly 106 in atleast one, or even both, of the two directions that are perpendicular tothe stacking direction D, by a factor of at least 5.

Similarly, in one embodiment, the first and second secondary growthconstraints 158, 160, respectively, of the primary growth constraintsystem 151 restrain growth of the electrode assembly 106 by exerting apressure on first and second opposing regions of the lateral surface 142of the electrode assembly 106 in a second direction orthogonal to thelongitudinal direction, such as first and second opposing surfaceregions along the vertical axis 148, 150, respectively (i.e., in avertical direction), that exceeds a pressure exerted by the first andsecond secondary growth constraints 158, 160, respectively, on othersurfaces of the electrode assembly 106 that would be in a directionorthogonal to the second direction. That is, the first and secondsecondary growth constraints 158, 160, respectively, may exert apressure in a vertical direction (Z axis) that exceeds a pressuregenerated thereby in directions orthogonal thereto, such as thetransverse (X axis) and longitudinal (Y axis) directions. For example,in one such embodiment, the secondary growth constraint system 152restrains growth of the electrode assembly 106 with a pressure on firstand second opposing surface regions 148, 150, respectively (i.e., in thevertical direction), that exceeds the pressure maintained on theelectrode assembly 106 by the secondary growth constraint system 152 inat least one, or even both, of the two directions that are perpendicularthereto, by a factor of at least 3. By way of further example, in onesuch embodiment, the secondary growth constraint system 152 restrainsgrowth of the electrode assembly 106 with a pressure on first and secondopposing surface regions 148, 150, respectively (i.e., in the verticaldirection), that exceeds the pressure maintained on the electrodeassembly 106 by the secondary growth constraint system 152 in at leastone, or even both, of the two directions that are perpendicular thereto,by a factor of at least 4. By way of further example, in one suchembodiment, the secondary growth constraint system 152 restrains growthof the electrode assembly 106 with a pressure on first and secondopposing surface regions 148, 150, respectively (i.e., in the verticaldirection), that exceeds the pressure maintained on the electrodeassembly 106 in at least one, or even both, of the two directions thatare perpendicular thereto, by a factor of at least 5.

In yet another embodiment, the first and second tertiary growthconstraints 157, 159, respectively, of the tertiary growth constraintsystem 155 restrain growth of the electrode assembly 106 by exerting apressure on first and second opposing regions of the lateral surface 142of the electrode assembly 106 in a direction orthogonal to thelongitudinal direction and the second direction, such as first andsecond opposing surface regions along the transverse axis 161, 163,respectively (i.e., in a transverse direction), that exceeds a pressureexerted by the tertiary growth constraint system 155 on other surfacesof the electrode assembly 106 that would be in a direction orthogonal tothe transverse direction. That is, the first and second tertiary growthconstraints 157, 159, respectively, may exert a pressure in a transversedirection (X axis) that exceeds a pressure generated thereby indirections orthogonal thereto, such as the vertical (Z axis) andlongitudinal (Y axis) directions. For example, in one such embodiment,the tertiary growth constraint system 155 restrains growth of theelectrode assembly 106 with a pressure on first and second opposingsurface regions 144, 146 (i.e., in the transverse direction) thatexceeds the pressure maintained on the electrode assembly 106 by thetertiary growth constraint system 155 in at least one, or even both, ofthe two directions that are perpendicular thereto, by a factor of atleast 3. By way of further example, in one such embodiment, the tertiarygrowth constraint system 155 restrains growth of the electrode assembly106 with a pressure on first and second opposing surface regions 144,146, respectively (i.e., in the transverse direction), that exceeds thepressure maintained on the electrode assembly 106 by the tertiary growthconstraint system 155 in at least one, or even both, of the twodirections that are perpendicular thereto, by a factor of at least 4. Byway of further example, in one such embodiment, the tertiary growthconstraint system 155 restrains growth of the electrode assembly 106with a pressure on first and second opposing surface regions 144, 146,respectively (i.e., in the transverse direction), that exceeds thepressure maintained on the electrode assembly 106 in at least one, oreven both, of the two directions that are perpendicular thereto, by afactor of at least 5.

In one embodiment, the set of electrode constraints 108, which mayinclude the primary growth constraint system 151, the secondary growthconstraint system 152, and optionally the tertiary growth constraintsystem 155, is configured to exert pressure on the electrode assembly106 along two or more dimensions thereof (e.g., along the longitudinaland vertical directions, and optionally along the transverse direction),with a pressure being exerted along the longitudinal direction by theset of electrode constraints 108 being greater than any pressure(s)exerted by the set of electrode constraints 108 in any of the directionsorthogonal to the longitudinal direction (e.g., the Z and X directions).That is, when the pressure(s) exerted by the primary, secondary, andoptionally tertiary growth constraint systems 151, 152, 155,respectively, making up the set of electrode constraints 108 are summedtogether, the pressure exerted on the electrode assembly 106 along thelongitudinal axis exceeds the pressure(s) exerted on the electrodeassembly 106 in the directions orthogonal thereto. For example, in onesuch embodiment, the set of electrode constraints 108 exerts a pressureon the first and second longitudinal end surfaces 116, 118 (i.e., in thestacking direction D) that exceeds the pressure maintained on theelectrode assembly 106 by the set of electrode constraints 108 in atleast one or even both of the two directions that are perpendicular tothe stacking direction D, by a factor of at least 3. By way of furtherexample, in one such embodiment, the set of electrode constraints 108exerts a pressure on first and second longitudinal end surfaces 116, 118(i.e., in the stacking direction D) that exceeds the pressure maintainedon the electrode assembly 106 by the set of electrode constraints 108 inat least one, or even both, of the two directions that are perpendicularto the stacking direction D by a factor of at least 4. By way of furtherexample, in one such embodiment, the set of electrode constraints 108exerts a pressure on first and second longitudinal end surfaces 116, 118(i.e., in the stacking direction D) that exceeds the pressure maintainedon the electrode assembly 106 in at least one, or even both, of the twodirections that are perpendicular to the stacking direction D, by afactor of at least 5.

According to one embodiment, the first and second longitudinal endsurfaces 116, 118, respectively, have a combined surface area that isless than a predetermined amount of the overall surface area of theentire electrode assembly 106. For example, in one embodiment, theelectrode assembly 106 may have a geometric shape corresponding to thatof a rectangular prism with first and second longitudinal end surfaces116, 118, respectively, and a lateral surface 142 extending between theend surfaces 116, 118, respectively, that makes up the remaining surfaceof the electrode assembly 106, and that has opposing surface regions144, 146 in the X direction (i.e., the side surfaces of the rectangularprism) and opposing surface regions 148, 150 in the Z direction (i.e.,the top and bottom surfaces of the rectangular prism, wherein X, Y and Zare dimensions measured in directions corresponding to the X, Y, and Zaxes, respectively). The overall surface area is thus the sum of thesurface area covered by the lateral surface 142 (i.e., the surface areaof the opposing surfaces 144, 146, 148, and 150 in X and Z), added tothe surface area of the first and second longitudinal end surfaces 116,118, respectively. In accordance with one aspect of the presentdisclosure, the sum of the surface areas of the first and secondlongitudinal end surfaces 116, 118, respectively, is less than 33% ofthe surface area of the total surface of the electrode assembly 106. Forexample, in one such embodiment, the sum of the surface areas of thefirst and second longitudinal end surfaces 116, 118, respectively, isless than 25% of the surface area of the total surface of the electrodeassembly 106. By way of further example, in one embodiment, the sum ofthe surface areas of the first and second longitudinal end surfaces 116,118, respectively, is less than 20% of the surface area of the totalsurface of the electrode assembly. By way of further example, in oneembodiment, the sum of the surface areas of the first and secondlongitudinal end surfaces 116, 118, respectively, is less than 15% ofthe surface area of the total surface of the electrode assembly. By wayof further example, in one embodiment, the sum of the surface areas ofthe first and second longitudinal end surfaces 116, 118, respectively,is less than 10% of the surface area of the total surface of theelectrode assembly.

In yet another embodiment, the electrode assembly 106 is configured suchthat a surface area of a projection of the electrode assembly 106 in aplane orthogonal to the stacking direction (i.e., the longitudinaldirection), is smaller than the surface areas of projections of theelectrode assembly 106 onto other orthogonal planes. For example,referring to the electrode assembly 106 embodiment shown in FIG. 1A(e.g., a rectangular prism), it can be seen that surface area of aprojection of the electrode assembly 106 into a plane orthogonal to thestacking direction (i.e., the X-Z plane) corresponds to L_(EA)×H_(EA).Similarly, a projection of the electrode assembly 106 into the Z-Y planecorresponds to W_(EA)×H_(EA), and a projection of the electrode assembly106 into the X-Y plane corresponds to L_(EA)×W_(EA). Accordingly, theelectrode assembly 106 is configured such that the stacking directionintersects the plane in which the projection having the smallest surfacearea lies. Accordingly, in the embodiment in FIG. 2, the electrodeassembly 106 is positioned such that the stacking direction intersectsthe X-Z plane in which the smallest surface area projectioncorresponding to H_(EA)×L_(EA) lies. That is, the electrode assembly ispositioned such that the projection having the smallest surface area(e.g., H_(EA)×L_(EA)) is orthogonal to the stacking direction.

In yet another embodiment, the secondary battery 102 can comprise aplurality of electrode assemblies 106 that are stacked together to forman electrode stack, and can be constrained by one or more sharedelectrode constraints. For example, in one embodiment, at least aportion of one or more of the primary growth constraint system 151 andthe secondary growth constraint system 152 can be shared by a pluralityof electrode assemblies 106 forming the electrode assembly stack. By wayof further example, in one embodiment, a plurality of electrodeassemblies forming an electrode assembly stack may be constrained in avertical direction by a secondary growth constraint system 152 having afirst secondary growth constraint 158 at a top electrode assembly 106 ofthe stack, and a second secondary growth constraint 160 at a bottomelectrode assembly 106 of the stack, such that the plurality ofelectrode assemblies 106 forming the stack are constrained in thevertical direction by the shared secondary growth constraint system.Similarly, portions of the primary growth constraint system 151 couldalso be shared. Accordingly, in one embodiment, similarly to the singleelectrode assembly described above, a surface area of a projection ofthe stack of electrode assemblies 106 in a plane orthogonal to thestacking direction (i.e., the longitudinal direction), is smaller thanthe surface areas of projections of the stack of electrode assemblies106 onto other orthogonal planes. That is, the plurality of electrodeassemblies 106 may be configured such that the stacking direction (i.e.,longitudinal direction) intersects and is orthogonal to a plane that hasa projection of the stack of electrode assemblies 106 that is thesmallest of all the other orthogonal projections of the electrodeassembly stack.

According to one embodiment, the electrode assembly 106 furthercomprises anode structures 110 that are configured such that a surfacearea of a projection of the anode structures 110 into a plane orthogonalto the stacking direction (i.e., the longitudinal direction), is largerthan the surface areas of projections of the electrode structures 100onto other orthogonal planes. For example, referring to the embodimentsas shown in FIGS. 1A and 7, the anodes 110 can each be understood tohave a length L_(A) measured in the transverse direction, a width W_(A)measured in the longitudinal direction, and a height H_(A) measured inthe vertical direction. The projection into the X-Z plane as shown inFIGS. 1A and 7 thus has a surface area L_(A)×H_(A), the projection intothe Y-Z plane has a surface area W_(A)×H_(A), and the projection intothe XY plane has a surface area L_(A)×WA. Of these, the planecorresponding to the projection having the largest surface area is theone that is selected to be orthogonal to the stacking direction.Similarly, the anodes 110 may also be configured such that a surfacearea of a projection of the anode active material layer 132 into a planeorthogonal to the stacking direction is larger than the surface areas ofprojections of the electrode active material layer onto other orthogonalplanes. For example, in the embodiments shown in FIGS. 1A and 7, theanode active material layer may have a length L_(AA) measured in thetransverse direction, a width W_(AA) measured in the longitudinaldirection, and a height H_(AA) measured in the vertical direction, fromthe surface areas of projections can be calculated (L_(A), L_(AA),W_(A), W_(AA), H_(A) and H_(AA) may also correspond to the maximum ofthese dimensions, in a case where the dimensions of the anode structureand/or anode active material layer 132 vary along one or more axes). Inone embodiment, by positioning the anode structures 110 such that theplane having the highest projection surface area of the anode structure110 and/or anode active material layer 132 is orthogonal to the stackingdirection, a configuration can be achieved whereby the surface of theanode structure 110 having the greatest surface area of anode activematerial faces the direction of travel of the carrier ions, and thusexperiences the greatest growth during cycling between charged anddischarged states due to intercalation and/or alloying.

In one embodiment, the anode structure 110 and electrode assembly 106can be configured such that the largest surface area projection of theanode structure 110 and/or anode active material layer 132, and thesmallest surface area projection of the electrode assembly 106 aresimultaneously in a plane that is orthogonal to the stacking direction.For example, in a case as shown in FIGS. 1A and 7, where the projectionof the anode active material layer 132 in the X-Z plane (L_(AA)×H_(AA))of the anode active material layer 132 is the highest, the anodestructure 110 and/or anode active material layer 132 is positioned withrespect to the smallest surface area projection of the electrodeassembly (L_(EA)×H_(EA)) such the projection plane for both projectionsis orthogonal to the stacking direction. That is, the plane having thegreatest surface area projection of the anode structure 110 and/or anodeactive material is parallel to (and/or in the same plane with) the planehaving the smallest surface area projection of the electrode assembly106. In this way, according to one embodiment, the surfaces of the anodestructures that are most likely to experience the highest volume growth,i.e., the surfaces having the highest content of anode active materiallayer, and/or surfaces that intersect (e.g., are orthogonal to) adirection of travel of carrier ions during charge/discharge of asecondary battery, face the surfaces of the electrode assembly 106having the lowest surface area. An advantage of providing such aconfiguration may be that the growth constraint system used to constrainin this greatest direction of growth, e.g. along the longitudinal axis,can be implemented with growth constraints that themselves have arelatively small surface area, as compared to the area of other surfacesof the electrode assembly 106, thereby reducing the volume required forimplementing a constraint system to restrain growth of the electrodeassembly.

In one embodiment, the constraint system 108 occupies a relatively lowvolume % of the combined volume of the electrode assembly 106 andconstraint system 108. That is, the electrode assembly 106 can beunderstood as having a volume bounded by its exterior surfaces (i.e.,the displacement volume), namely the volume enclosed by the first andsecond longitudinal end surfaces 116, 118 and the lateral surface 42connecting the end surfaces. Portions of the constraint system 108 thatare external to the electrode assembly 106 (i.e., external to thelongitudinal end surfaces 116, 118 and the lateral surface), such aswhere first and second primary growth constraints 154, 156 are locatedat the longitudinal ends 117, 119 of the electrode assembly 106, andfirst and second secondary growth constraints 158, 160 are at theopposing ends of the lateral surface 142, the portions of the constrainsystem 108 similarly occupy a volume corresponding to the displacementvolume of the constraint system portions. Accordingly, in oneembodiment, the external portions of the set of electrode constraints108, which can include external portions of the primary growthconstraint system 151 (i.e., any of the first and second primary growthconstraints 154, 156 and at least one primary connecting member that areexternal, or external portions thereof), as well as external portions ofthe secondary growth constraint system 152 (i.e., any of the first andsecond secondary growth constraints 158, 160 and at least one secondaryconnecting member that are external, or external portions thereof)occupies no more than 80% of the total combined volume of the electrodeassembly 106 and external portion of the set of electrode constraints108. By way of further example, in one embodiment the external portionsof the set of electrode constraints occupies no more than 60% of thetotal combined volume of the electrode assembly 106 and the externalportion of the set of electrode constraints. By way of yet a furtherexample, in one embodiment the external portion of the set of electrodeconstraints 106 occupies no more than 40% of the total combined volumeof the electrode assembly 106 and the external portion of the set ofelectrode constraints. By way of yet a further example, in oneembodiment the external portion of the set of electrode constraints 106occupies no more than 20% of the total combined volume of the electrodeassembly 106 and the external portion of the set of electrodeconstraints. In yet another embodiment, the external portion of theprimary growth constraint system 151 (i.e., any of the first and secondprimary growth constraints 154, 156 and at least one primary connectingmember that are external, or external portions thereof) occupies no morethan 40% of the total combined volume of the electrode assembly 106 andthe external portion of the primary growth constraint system 151. By wayof further example, in one embodiment the external portion of theprimary growth constraint system 151 occupies no more than 30% of thetotal combined volume of the electrode assembly 106 and the externalportion of the primary growth constraint system 151. By way of yet afurther example, in one embodiment the external portion of the primarygrowth constraint system 151 occupies no more than 20% of the totalcombined volume of the electrode assembly 106 and the external portionof the primary growth constraint system 151. By way of yet a furtherexample, in one embodiment the external portion of the primary growthconstraint system 151 occupies no more than 10% of the total combinedvolume of the electrode assembly 106 and the external portion of theprimary growth constraint system 151. In yet another embodiment, theexternal portion of the secondary growth constraint system 152 (i.e.,any of the first and second secondary growth constraints 158, 160 and atleast one secondary connecting member that are external, or externalportions thereof) occupies no more than 40% of the total combined volumeof the electrode assembly 106 and the external portion of the secondarygrowth constraint system 152. By way of further example, in oneembodiment, the external portion of the secondary growth constraintsystem 152 occupies no more than 30% of the total combined volume of theelectrode assembly 106 and the external portion of the secondary growthconstraint system 152. By way of yet another example, in one embodiment,the external portion of the secondary growth constraint system 152occupies no more than 20% of the total combined volume of the electrodeassembly 106 and the external portion of the secondary growth constraintsystem 152. By way of yet another example, in one embodiment, theexternal portion of the secondary growth constraint system 152 occupiesno more than 10% of the total combined volume of the electrode assembly106 and the external portion of the secondary growth constraint system152.

According to one embodiment, a projection of the members of the anodeand cathode populations onto first and second longitudinal end surfaces116, 118 circumscribes a first and second projected area 2002 a, 2002 b.In general, first and second projected areas 2002 a, 2002 b willtypically comprise a significant fraction of the surface area of thefirst and second longitudinal end surfaces 122, 124, respectively. Forexample, in one embodiment the first and second projected areas eachcomprise at least 50% of the surface area of the first and secondlongitudinal end surfaces, respectively. By way of further example, inone such embodiment the first and second projected areas each compriseat least 75% of the surface area of the first and second longitudinalend surfaces, respectively. By way of further example, in one suchembodiment the first and second projected areas each comprise at least90% of the surface area of the first and second longitudinal endsurfaces, respectively.

In certain embodiments, the longitudinal end surfaces 116, 118 of theelectrode assembly 106 will be under a significant compressive load. Forexample, in some embodiments, each of the longitudinal end surfaces 116,118 of the electrode assembly 106 will be under a compressive load of atleast 0.7 kPa (e.g., averaged over the total surface area of each of thelongitudinal end surfaces, respectively). For example, in oneembodiment, each of the longitudinal end surfaces 116, 118 of theelectrode assembly 106 will be under a compressive load of at least 1.75kPa (e.g., averaged over the total surface area of each of thelongitudinal end surfaces, respectively). By way of further example, inone such embodiment, each of the longitudinal end surfaces 116, 118 ofthe electrode assembly 106 will be under a compressive load of at least2.8 kPa (e.g., averaged over the total surface area of each of thelongitudinal end surfaces, respectively). By way of further example, inone such embodiment, each of the longitudinal end surfaces 116, 118 ofthe electrode assembly 106 will be under a compressive load of at least3.5 kPa (e.g., averaged over the total surface area of each of thelongitudinal end surfaces, respectively). By way of further example, inone such embodiment, each of the longitudinal end surfaces 116, 118 ofthe electrode assembly 106 will be under a compressive load of at least5.25 kPa (e.g., averaged over the total surface area of each of thelongitudinal end surfaces, respectively). By way of further example, inone such embodiment, each of the longitudinal end surfaces 116, 118 ofthe electrode assembly 106 will be under a compressive load of at least7 kPa (e.g., averaged over the total surface area of each of thelongitudinal end surfaces, respectively). By way of further example, inone such embodiment, each of the longitudinal end surfaces 116, 118 ofthe electrode assembly 106 will be under a compressive load of at least8.75 kPa (e.g., averaged over the total surface area of each of thelongitudinal end surfaces, respectively). In general, however, thelongitudinal end surfaces 116, 118 of the electrode assembly 106 will beunder a compressive load of no more than about 10 kPa (e.g., averagedover the total surface area of each of the longitudinal end surfaces,respectively). The regions of the longitudinal end surface of theelectrode assembly that are coincident with the projection of members ofthe electrode and counter-electrode populations onto the longitudinalend surfaces (i.e., the projected surface regions) may also be under theabove compressive loads (as averaged over the total surface area of eachprojected surface region, respectively). In each of the foregoingexemplary embodiments, the longitudinal end surfaces 116, 118 of theelectrode assembly 106 will experience such compressive loads when anenergy storage device 100 having the electrode assembly 106 is chargedto at least about 80% of its rated capacity.

According to one embodiment, the secondary growth constraint system 152is capable of restraining growth of the electrode assembly 106 in thevertical direction (Z direction) by applying a restraining force at apredetermined value, and without excessive skew of the growthrestraints. For example, in one embodiment, the secondary growthconstraint system 152 may restrain growth of the electrode assembly 106in the vertical direction by applying a restraining force to opposingvertical regions 148, 150 of greater than 1000 psi and a skew of lessthan 0.2 mm/m. By way of further example, in one embodiment, thesecondary growth constraint system 152 may restrain growth of theelectrode assembly 106 in the vertical direction by applying arestraining force to opposing vertical regions 148, 150 with less than5% displacement at less than or equal to 10,000 psi and a skew of lessthan 0.2 mm/m. By way of further example, in one embodiment, thesecondary growth constraint system 152 may restrain growth of theelectrode assembly 106 in the vertical direction by applying arestraining force to opposing vertical regions 148, 150 with less than3% displacement at less than or equal to 10,000 psi and a skew of lessthan 0.2 mm/m. By way of further example, in one embodiment, thesecondary growth constraint system 152 may restrain growth of theelectrode assembly 106 in the vertical direction by applying arestraining force to opposing vertical regions 148, 150 with less than1% displacement at less than or equal to 10,000 psi and a skew of lessthan 0.2 mm/m. By way of further example, in one embodiment, thesecondary growth constraint system 152 may restrain growth of theelectrode assembly 106 in the vertical direction by applying arestraining force to opposing vertical regions 148, 150 in the verticaldirection with less than 15% displacement at less than or equal to10,000 psi and a skew of less than 0.2 mm/m after 50 battery cycles. Byway of further example, in one embodiment, the secondary growthconstraint system 152 may restrain growth of the electrode assembly 106in the vertical direction by applying a restraining force to opposingvertical regions 148, 150 with less than 5% displacement at less than orequal to 10,000 psi and a skew of less than 0.2 mm/m after 150 batterycycles.

Referring now to FIG. 6D, an embodiment of an electrode assembly 106with a set of electrode constraints 108 is shown, with a cross-sectiontaken along the line A-A′ as shown in FIG. 1B. In the embodiment shownin FIG. 6D, the primary growth constraint system 151 can comprise firstand second primary growth constraints 154, 156, respectively, at thelongitudinal end surfaces 116, 118 of the electrode assembly 106, andthe secondary growth constraint system 152 comprises first and secondsecondary growth constraints 158, 160 at the opposing first and secondsurface regions 148, 150 of the lateral surface 142 of the electrodeassembly 106. According to this embodiment, the first and second primarygrowth constraints 154, 156 can serve as the at least one secondaryconnecting member 166 to connect the first and second secondary growthconstrains 158, 160 and maintain the growth constraints in tension withone another in the second direction (e.g., vertical direction) that isorthogonal to the longitudinal direction. However, additionally and/oralternatively, the secondary growth constraint system 152 can compriseat least one secondary connecting member 166 that is located at a regionother than the longitudinal end surfaces 116, 118 of the electrodeassembly 106. Also, the at least one secondary connecting member 166 canbe understood to act as at least one of a first and second primarygrowth constraint 154, 156 that is internal to the longitudinal ends116, 118 of the electrode assembly, and that can act in conjunction witheither another internal primary growth restraint and/or a primary growthrestraint at a longitudinal end 116, 118 of the electrode assembly 106to restrain growth. Referring to the embodiment shown in FIG. 6D, asecondary connecting member 166 can be provided that is spaced apartalong the longitudinal axis away from the first and second longitudinalend surfaces 116, 118, respectively, of the electrode assembly 106, suchas toward a central region of the electrode assembly 106. The secondaryconnecting member 166 can connect the first and second secondary growthconstraints 158, 160, respectively, at an interior position from theelectrode assembly end surfaces 116, 118, and may be under tensionbetween the secondary growth constraints 158, 160 at that position. Inone embodiment, the secondary connecting member 166 that connects thesecondary growth constraints 158, 160 at an interior position from theend surfaces 116, 118 is provided in addition to one or more secondaryconnecting members 166 provided at the electrode assembly end surfaces116, 118, such as the secondary connecting members 166 that also serveas primary growth constraints 154, 156 at the longitudinal end surfaces116, 118. In another embodiment, the secondary growth constraint system152 comprises one or more secondary connecting members 166 that connectwith first and second secondary growth constraints 158, 160,respectively, at interior positions that are spaced apart from thelongitudinal end surfaces 116, 118, with or without secondary connectingmembers 166 at the longitudinal end surfaces 116, 118. The interiorsecondary connecting members 166 can also be understood to act as firstand second primary growth constraints 154, 156, according to oneembodiment. For example, in one embodiment, at least one of the interiorsecondary connecting members 166 can comprise at least a portion of ananode or cathode structure 110, 112, as described in further detailbelow.

More specifically, with respect to the embodiment shown in FIG. 6D,secondary growth constraint system 152 may include a first secondarygrowth constraint 158 that overlies an upper region 148 of the lateralsurface 142 of electrode assembly 106, and an opposing second secondarygrowth constraint 160 that overlies a lower region 150 of the lateralsurface 142 of electrode assembly 106, the first and second secondarygrowth constraints 158, 160 being separated from each other in thevertical direction (i.e., along the Z-axis). Additionally, secondarygrowth constraint system 152 may further include at least one interiorsecondary connecting member 166 that is spaced apart from thelongitudinal end surfaces 116, 118 of the electrode assembly 106. Theinterior secondary connecting member 166 may be aligned parallel to theZ axis and connects the first and second secondary growth constraints158, 160, respectively, to maintain the growth constraints in tensionwith one another, and to form at least a portion of the secondaryconstraint system 152. In one embodiment, the at least one interiorsecondary connecting member 166, either alone or with secondaryconnecting members 166 located at the longitudinal end surfaces 116, 118of the electrode assembly 106, may be under tension between the firstand secondary growth constraints 158, 160 in the vertical direction(i.e., along the Z axis), during repeated charge and/or discharge of anenergy storage device 100 or a secondary battery 102 having theelectrode assembly 106, to reduce growth of the electrode assembly 106in the vertical direction. Furthermore, in the embodiment as shown inFIG. 5, the set of electrode constraints 108 further comprises a primarygrowth constraint system 151 having first and second primary growthconstraints 154, 156, respectively, at the longitudinal ends 117, 119 ofthe electrode assembly 106, that are connected by first and secondprimary connecting members 162, 164, respectively, at the upper andlower lateral surface regions 148, 150, respectively, of the electrodeassembly 106. In one embodiment, the secondary interior connectingmember 166 can itself be understood as acting in concert with one ormore of the first and second primary growth constraints 154, 156,respectively, to exert a constraining pressure on each portion of theelectrode assembly 106 lying in the longitudinal direction between thesecondary interior connecting member 166 and the longitudinal ends 117,119 of the electrode assembly 106 where the first and second primarygrowth constraints 154, 156, respectively, can be located.

In one embodiment, one or more of the primary growth constraint system151 and secondary growth constraint system 152 includes first andsecondary primary growth constraints 154, 156, respectively, and/orfirst and second secondary growth constraints 158, 160, respectively,that include a plurality of constraint members. That is, each of theprimary growth constraints 154, 156 and/or secondary growth constraints158, 160 may be a single unitary member, or a plurality of members maybe used to make up one or more of the growth constraints. For example,in one embodiment, the first and second secondary growth constraints158, 160, respectively, can comprise single constraint members extendingalong the upper and lower surface regions 148, 150, respectively, of theelectrode assembly lateral surface 142. In another embodiment, the firstand second secondary growth constraints 158, 160, respectively, comprisea plurality of members extending across the opposing surface regions148, 150, of the lateral surface. Similarly, the primary growthconstraints 154, 156 may also be made of a plurality of members, or caneach comprise a single unitary member at each electrode assemblylongitudinal end 117, 119. To maintain tension between each of theprimary growth constraints 154, 156 and secondary growth constraints158, 160, the connecting members (e.g., 162, 164, 165, 166) are providedto connect the one or plurality of members comprising the growthconstraints to the opposing growth constraint members in a manner thatexerts pressure on the electrode assembly 106 between the growthconstraints.

In one embodiment, the at least one secondary connecting member 166 ofthe secondary growth constraint system 152 forms areas of contact 168,170 with the first and second secondary growth constraints 158, 160,respectively, to maintain the growth constraints in tension with oneanother. The areas of contact 168, 170 are those areas where thesurfaces at the ends 172, 174 of the at least one secondary connectingmember 166 touches and/or contacts the first and second secondary growthconstraints 158, 160, respectively, such as where a surface of an end ofthe at least one secondary connecting member 166 is adhered or glued tothe first and second secondary growth constraints 158, 160,respectively. The areas of contact 168, 170 may be at each end 172, 174and may extend across a surface area of the first and second secondarygrowth constraints 158, 160, to provide good contact therebetween. Theareas of contact 168, 170 provide contact in the longitudinal direction(Y axis) between the second connecting member 166 and the growthconstraints 158, 160, and the areas of contact 168, 170 can also extendinto the transverse direction (X-axis) to provide good contact andconnection to maintain the first and second secondary growth constraints158, 160 in tension with one another. In one embodiment, the areas ofcontact 168, 170 provide a ratio of the total area of contact (e.g., thesum of all areas 168, and the sum of all areas 170) of the one or moresecondary connecting members 166 in the longitudinal direction (Y axis)with the growth constraints 158, 160, per W_(EA) of the electrodeassembly 106 in the longitudinal direction that is at least 1%. Forexample, in one embodiment, a ratio of the total area of contact of theone or more secondary connecting members 166 in the longitudinaldirection (Y axis) with the growth constraints 158, 160, per W_(EA) ofthe electrode assembly 106 in the longitudinal direction is at least 2%.By way of further example, in one embodiment, a ratio of the total areaof contact of the one or more secondary connecting members 166 in thelongitudinal direction (Y axis) with the growth constraints 158, 160,per W_(EA) of the electrode assembly 106 in the longitudinal direction,is at least 5%. By way of further example, in one embodiment, a ratio ofthe total area of contact of the one or more secondary connectingmembers 166 in the longitudinal direction (Y axis) with the growthconstraints 158, 160, per W_(EA) of the electrode assembly 106 in thelongitudinal direction, is at least 10%. By way of further example, inone embodiment, a ratio of the total area of contact of the one or moresecondary connecting members 166 in the longitudinal direction (Y axis)with the growth constraints 158, 160, per W_(EA) of the electrodeassembly 106 in the longitudinal direction, is at least 25%. By way offurther example, in one embodiment, a ratio of the total area of contactof the one or more secondary connecting members 166 in the longitudinaldirection (Y axis) with the growth constraints 158, 160, per W_(EA) ofthe electrode assembly 106 in the longitudinal direction, is at least50%. In general, a ratio of the total area of contact of the one or moresecondary connecting members 166 in the longitudinal direction (Y axis)with the growth constraints 158, 160, per W_(EA) of the electrodeassembly 106 in the longitudinal direction, will be less than 100%, suchas less than 90%, and even less than 75%, as the one or more connectingmembers 166 typically do not have an area of contact 168, 170 thatextends across the entire longitudinal axis. However, in one embodiment,an area of contact 168, 170 of the secondary connecting members 166 withthe growth constraints 158, 160, may extend across a significant portionof the transverse axis (X axis), and may even extend across the entireL_(EA) of the electrode assembly 106 in the transverse direction. Forexample, a ratio of the total area of contact (e.g., the sum of allareas 168, and the sum of all areas 170) of the one or more secondaryconnecting members 166 in the transverse direction (X axis) with thegrowth constraints 158, 160, per L_(EA) of the electrode assembly 106 inthe transverse direction, may be at least about 50%. By way of furtherexample, a ratio of the total area of contact of the one or moresecondary connecting members 166 in the transverse direction (X axis)with the growth constraints 158, 160, per L_(EA) of the electrodeassembly 106 in the transverse direction (X-axis), may be at least about75%. By way of further example, a ratio of the total area of contact ofthe one or more secondary connecting members 166 in the transversedirection (X axis) with the growth constraints 158, 160, per L_(EA) ofthe electrode assembly 106 in the transverse direction (X axis), may beat least about 90%. By way of further example, a ratio of the total areaof contact of the one or more secondary connecting members 166 in thetransverse direction (X axis) with the growth constraints 158, 160, perL_(EA) of the electrode assembly 106 in the transverse direction (Xaxis), may be at least about 95%.

According to one embodiment, the areas of contact 168, 170 between theone or more secondary connecting members 166 and the first and secondsecondary growth constraints 158, 160, respectively, are sufficientlylarge to provide for adequate hold and tension between the growthconstraints 158, 160 during cycling of an energy storage device 100 or asecondary battery 102 having the electrode assembly 106. For example,the areas of contact 168, 170 may form an area of contact with eachgrowth constraint 158, 160 that makes up at least 2% of the surface areaof the lateral surface 142 of the electrode assembly 106, such as atleast 10% of the surface area of the lateral surface 142 of theelectrode assembly 106, and even at least 20% of the surface area of thelateral surface 142 of the electrode assembly 106. By way of furtherexample, the areas of contact 168, 170 may form an area of contact witheach growth constraint 158, 160 that makes up at least 35% of thesurface area of the lateral surface 142 of the electrode assembly 106,and even at least 40% of the surface area of the lateral surface 142 ofthe electrode assembly 106. For example, for an electrode assembly 106having upper and lower opposing surface regions 148, 150, respectively,the at least one secondary connecting member 166 may form areas ofcontact 168, 170 with the growth constraints 158, 160 along at least 5%of the surface area of the upper and lower opposing surface regions 148,150, respectively, such as along at least 10% of the surface area of theupper and lower opposing surface regions 148, 150, respectively, andeven at least 20% of the surface area of the upper and lower opposingsurface regions 148, 150, respectively. By way of further example, anelectrode assembly 106 having upper and lower opposing surface regions148, 150, respectively, the at least one secondary connecting member 166may form areas of contact 168, 170 with the growth constraints 158, 160along at least 40% of the surface area of the upper and lower opposingsurface regions 148, 150, respectively, such as along at least 50% ofthe surface area of the upper and lower opposing surface regions 148,150, respectively. By forming a contact between the at least oneconnecting member 166 and the growth constraints 158, 160 that makes upa minimum surface area relative to a total surface area of the electrodeassembly 106, proper tension between the growth constraints 158, 160 canbe provided. Furthermore, according to one embodiment, the areas ofcontact 168, 170 can be provided by a single secondary connecting member166, or the total area of contact may be the sum of multiple areas ofcontact 168, 170 provided by a plurality of secondary connecting members166, such as one or a plurality of secondary connecting members 166located at longitudinal ends 117, 119 of the electrode assembly 106,and/or one or a plurality of interior secondary connecting members 166that are spaced apart from the longitudinal ends 117, 119 of theelectrode assembly 106.

Further still, in one embodiment, the primary and secondary growthconstraint systems 151, 152, respectively, (and optionally the tertiarygrowth constraint system) are capable of restraining growth of theelectrode assembly 106 in both the longitudinal direction and the seconddirection orthogonal to the longitudinal direction, such as the verticaldirection (Z axis) (and optionally in the third direction, such as alongthe X axis), to restrain a volume growth % of the electrode assembly.

In certain embodiments, one or more of the primary and secondary growthconstraint systems 151, 152, respectively, comprises a member havingpores therein, such as a member made of a porous material. For example,referring to FIG. 8 depicting a top view of a secondary growthconstraint 158 over an electrode assembly 106, the secondary growthconstraint 158 can comprise pores 176 that permit electrolyte to passtherethrough, so as to access an electrode assembly 106 that is at leastpartially covered by the secondary growth constraint 158. In oneembodiment, the first and second secondary growth constraints 158, 160,respectively, have the pores 176 therein. In another embodiment, each ofthe first and second primary growth constraints 154, 156, respectively,and the first and second secondary growth constraints 158, 160,respectively, have the pores 176 therein. In yet another embodiment,only one or only a portion of the first and second secondary growthconstraints 158, 160, respectively, contain the pores therein. In yet afurther embodiment, one or more of the first and second primaryconnecting members 162, 164, respectively, and the at least onesecondary connecting member 166 contains pores therein. Providing thepores 176 may be advantageous, for example, when the energy storagedevice 100 or secondary battery 102 contains a plurality of electrodeassemblies 106 stacked together in the battery enclosure 104, to permitelectrolyte to flow between the different electrode assemblies 106 in,for example, the secondary battery 102 as shown in the embodimentdepicted in FIG. 9. For example, in one embodiment, a porous membermaking up at least a portion of the primary and secondary growthconstraint system 151, 152, respectively, may have a void fraction of atleast 0.25. By way of further example, in some embodiments, a porousmember making up at least a portion of the primary and secondary growthconstraint systems 151, 152, respectively, may have a void fraction ofat least 0.375. By way of further example, in some embodiments, a porousmember making up at least a portion of the primary and secondary growthconstraint systems 151, 152, respectively, may have a void fraction ofat least 0.5. By way of further example, in some embodiments, a porousmember making up at least a portion of the primary and secondary growthconstraint systems 151, 152, respectively, may have a void fraction ofat least 0.625. By way of further example, in some embodiments, a porousmember making up at least a portion of the primary and secondary growthconstraint systems 151, 152, respectively, may have a void fraction ofat least 0.75.

In one embodiment, the set of electrode constraints 108 may be assembledand secured to restrain growth of the electrode assembly 106 by at leastone of adhering, bonding, and/or gluing components of the primary growthconstraint system 151 to components of the secondary growth constraintsystem 152. For example, components of the primary growth constraintsystem 151 may be glued, welded, bonded, or otherwise adhered andsecured to components of the secondary growth constraint system 152. Forexample, as shown in FIG. 6A, the first and second primary growthconstraints 154, 156, respectively, can be adhered to first and secondprimary connecting members 162, 164, respectively, that may also serveas first and second secondary growth constraints 158, 160, respectively.Conversely, the first and second secondary growth constraints 158, 150,respectively, can be adhered to at least one secondary connecting member166 that serves as at least one of the first and second primary growthconstraints 154, 156, respectively, such as growth constraints at thelongitudinal ends 117, 119 of the electrode assembly 106. Referring toFIG. 6D, the first and second secondary growth constraints 158, 160,respectively, can also be adhered to at least one secondary connectingmember 166 that is an interior connecting member 166 spaced apart fromthe longitudinal ends 117, 119. In one embodiment, by securing portionsof the primary and secondary growth constraint systems 151, 152,respectively, to one another, the cooperative restraint of the electrodeassembly 106 growth can be provided.

Constraint System Sub-Architecture

According to one embodiment, as discussed above, one or more of thefirst and second secondary growth constraints 158, 160, respectively,can be connected together via a secondary connecting member 166 that isa part of an interior structure of the electrode assembly 106, such as apart of an anode 110 and/or cathode structure 112. In one embodiment, byproviding connection between the constraints via structures within theelectrode assembly 106, a tightly constrained structure can be realizedthat adequately compensates for strain produced by growth of the anodestructure 110. For example, in one embodiment, the first and secondsecondary growth constraints 158, 160, respectively, may constraingrowth in a direction orthogonal to the longitudinal direction, such asthe vertical direction, by being placed in tension with one another viaconnection through a connecting member 166 that is a part of an anode110 or cathode structure 112. In yet a further embodiment, growth of ananode structure 110 can be countered by connection of the secondarygrowth constraints 158, 160 through a cathode structure 112 that servesas the secondary connecting member 166.

In general, in certain embodiments, components of the primary growthconstraint system 151 and the secondary growth constraint system 152 maybe attached to the anode 110 and/or cathode structures 112,respectively, within an electrode assembly 106, and components of thesecondary growth constraint system 152 may also be embodied as the anode110 and/or cathode structures 112, respectively, within an electrodeassembly 106, not only to provide effective restraint but also to moreefficiently utilize the volume of the electrode assembly 106 withoutexcessively increasing the size of an energy storage device 110 or asecondary battery 102 having the electrode assembly 106. For example, inone embodiment, the primary growth constraint system 151 and/orsecondary growth constraint system 152 may be attached to one or moreanode structures 110. By way of further example, in one embodiment, theprimary growth constraint system 151 and/or secondary growth constraintsystem 152 may be attached to one or more cathode structures 112. By wayof further example, in certain embodiments, the at least one secondaryconnecting member 166 may be embodied as the population of anodestructures 110. By way of further example, in certain embodiments, theat least one secondary connecting member 166 may be embodied as thepopulation of cathode structures 112.

Referring now to FIG. 7, a Cartesian coordinate system is shown forreference having a vertical axis (Z axis), a longitudinal axis (Y axis),and a transverse axis (X axis); wherein the X axis is oriented as comingout of the plane of the page; and a designation of the stackingdirection D, as described above, co-parallel with the Y axis. Morespecifically, FIG. 7 shows a cross section, along the line A-A′ as inFIG. 1B, of a set of electrode constraints 108, including one embodimentof both a primary growth constraint system 151 and one embodiment of asecondary growth constraint system 152. Primary growth constraint system151 includes a first primary growth constraint 154 and a second primarygrowth constraint 156, as described above, and a first primaryconnecting member 162 and a second primary connecting member 164, asdescribed above. Secondary growth constraint system 152 includes a firstsecondary growth constraint 158, a second secondary growth constraint160, and at least one secondary connecting member 166 embodied as thepopulation of anode structures 110 and/or the population of cathodestructures 112; therefore, in this embodiment, the at least onesecondary connecting member 166, anode structures 110, and/or cathodestructures 112 can be understood to be interchangeable. Furthermore, theseparator 130 may also form a portion of a secondary connecting member166. Further, in this embodiment, first primary connecting member 162and first secondary growth constraint 158 are interchangeable, asdescribed above. Further still, in this embodiment, second primaryconnecting member 164 and second secondary growth constraint 160 areinterchangeable, as described above. More specifically, illustrated inFIG. 7 is one embodiment of a flush connection of the secondaryconnecting member 166 corresponding to the anode 110 or cathodestructure 112 with the first secondary growth constraint 158 and secondsecondary growth constraint 160. The flush connection may furtherinclude a layer of glue 182 between the first secondary growthconstraint 158 and secondary connecting member 166, and a layer of glue182 between the second secondary growth constraint 160 and secondaryconnecting member 166. The layers of glue 182 affix first secondarygrowth constraint 158 to secondary connecting members 166, and affix thesecond secondary growth constraint 160 to secondary connecting member166.

Also, one or more of the first and second primary growth constraints154, 156, first and second primary connecting members 162, 164, firstand second secondary growth constraints 158, 160, and at least onesecondary connecting member 166 may be provided in the form of aplurality of segments 1088 or parts that can be joined together to forma single member. For example, as shown in the embodiment as illustratedin FIG. 7, a first secondary growth constraint 158 is provided in theform of a main middle segment 1088 a and first and second end segments1088 b located towards the longitudinal ends 117, 119 of the electrodeassembly 106, with the middle segment 1088 a being connected to eachfirst and second end segment 1088 b by a connecting portion 1089provided to connect the segments 1088, such as notches formed in thesegments 1088 that can be interconnected to join the segments 1088 toone another. A second secondary growth constraint 160 may similarly beprovided in the form of a plurality of segments 1088 that can beconnected together to form the constraint, as shown in FIG. 7. In oneembodiment, one or more of the secondary growth constraints 158, 160, atleast one primary connecting member 162, and/or at least one secondaryconnecting member 166 may also be provided in the form of a plurality ofsegments 1088 that can be connected together via a connecting portionssuch as notches to form the complete member. According to oneembodiment, the connection of the segments 1088 together via the notchor other connecting portion may provide for pre-tensioning of the memberformed of the plurality of segments when the segments are connected.

Further illustrated in FIG. 7, in one embodiment, are members of theanode population 110 having an anode active material layer 132, anionically porous anode current collector 136, and an anode backbone 134that supports the anode active material layer 132 and the anode currentcollector 136. Similarly, in one embodiment, illustrated in FIG. 7 aremembers of the cathode population 112 having a cathode active materiallayer 138, a cathode collector 140, and a cathode backbone 141 thatsupports the cathode active material layer 138 and the cathode currentcollector 140.

While members of the anode population 110 have been illustrated anddescribed herein to include the anode active material layer 132 beingdirectly adjacent to the anode backbone 134, and the anode currentcollector 136 directly adjacent to and effectively surrounding the anodebackbone 134 and the anode active material layer 132, those of skill inthe art will appreciate other arrangements of the anode population 110have been contemplated. For example, in one embodiment (not shown), theanode population 110 may include the anode active material layer 132being directly adjacent to the anode current collector 136, and theanode current collector 136 being directly adjacent to the anodebackbone 134. Stated alternatively, the anode backbone 134 may beeffectively surrounded by the anode current collector 136, with theanode active material layer 132 flanking and being directly adjacent tothe anode current collector 136. As will be appreciated by those ofskill in the art, any suitable configuration of the anode population 110and/or the cathode population 112 may be applicable to the inventivesubject matter described herein, so long as the anode active materiallayer 132 is separated from the cathode active material layer 138 viaseparator 130. Also, the anode current collector 136 is required to beion permeable if it is located between the anode active material layer132 and separator 130; and the cathode current collector 140 is requiredto be ion permeable if it is located between the cathode active materiallayer 138 and separator 130.

For ease of illustration, only three members of the anode population 110and four members of the cathode population 112 are depicted; inpractice, however, an energy storage device 100 or secondary battery 102using the inventive subject matter herein may include additional membersof the anode 110 and cathode 112 populations depending on theapplication of the energy storage device 100 or secondary battery 102,as described above. Further still, illustrated in FIG. 7 is amicroporous separator 130 electrically insulating the anode activematerial layer 132 from the cathode active material layer 138.

Furthermore, to connect the first and second secondary growthconstraints 158, 160, respectively, the constraints 158, 160 can beattached to the at least one connecting member 166 by a suitable means,such as by gluing as shown, or alternatively by being welded, such as bybeing welded to the current collectors 136, 140. For example, the firstand/or second secondary growth constraints 158, 160, respectively, canbe attached to a secondary connecting member 166 corresponding to atleast one of an anode structure 110 and/or cathode structure 112, suchas at least one of an anode and/or cathode backbone 134, 141,respectively, an anode and/or cathode current collector 136, 140,respectively, by at least one of adhering, gluing, bonding, welding, andthe like. According to one embodiment, the first and/or second secondarygrowth constraints 158, 160, respectively, can be attached to thesecondary connecting member 166 by mechanically pressing the firstand/or second secondary growth constraint 158, 160, respectively, to anend of one or more secondary connecting member 166, such as ends of thepopulation of anode 100 and/or cathode structures 112, while using aglue or other adhesive material to adhere one or more ends of the anode110 and/or cathode structures 112 to at least one of the first and/orsecond secondary growth constraints 158, 160, respectively.

Population of Anode Structures

Referring again to FIG. 7, each member of the population of anodestructures 110 may also include a top 1052 adjacent to the firstsecondary growth constraint 158, a bottom 1054 adjacent to the secondsecondary growth constraint 160, and a lateral surface (not marked)surrounding a vertical axis A_(ES) (not marked) parallel to the Z axis,the lateral surface connecting the top 1052 and the bottom 1054. Theanode structures 110 further include a length L_(A), a width W_(A), anda height H_(A). The length L_(A) being bounded by the lateral surfaceand measured along the X axis. The width W_(A) being bounded by thelateral surface and measured along the Y axis, and the height H_(A)being measured along the vertical axis A_(ES) or the Z axis from the top1052 to the bottom 1054.

The L_(A) of the members of the anode population 110 will vary dependingupon the energy storage device 100 or the secondary battery 102 andtheir intended use(s). In general, however, the members of the anodepopulation 110 will typically have a L_(A) in the range of about 5 mm toabout 500 mm. For example, in one such embodiment, the members of theanode population 110 have a L_(A) of about 10 mm to about 250 mm. By wayof further example, in one such embodiment, the members of the anodepopulation 110 have a L_(A) of about 20 mm to about 100 mm.

The W_(A) of the members of the anode population 110 will also varydepending upon the energy storage device 100 or the secondary battery102 and their intended use(s). In general, however, each member of theanode population 110 will typically have a W_(A) within the range ofabout 0.01 mm to 2.5 mm. For example, in one embodiment, the W_(A) ofeach member of the anode population 110 will be in the range of about0.025 mm to about 2 mm. By way of further example, in one embodiment,the W_(A) of each member of the anode population 110 will be in therange of about 0.05 mm to about 1 mm.

The H_(A) of the members of the anode population 110 will also varydepending upon the energy storage device 100 or the secondary battery102 and their intended use(s). In general, however, members of the anodepopulation 110 will typically have a H_(A) within the range of about0.05 mm to about 10 mm. For example, in one embodiment, the H_(A) ofeach member of the anode population 110 will be in the range of about0.05 mm to about 5 mm. By way of further example, in one embodiment, theH_(A) of each member of the anode population 110 will be in the range ofabout 0.1 mm to about 1 mm.

In another embodiment, each member of the population of anode structures110 may include an anode structure backbone 134 having a vertical axisA_(ESB) parallel to the Z axis. The anode structure backbone 134 mayalso include a layer of anode active material 132 surrounding the anodestructure backbone 134 about the vertical axis A_(ESB). Statedalternatively, the anode structure backbone 134 provides mechanicalstability for the layer of anode active material 132, and may provide apoint of attachment for the primary growth constraint system 151 and/orsecondary constraint system 152. In certain embodiments, the layer ofanode active material 132 expands upon insertion of carrier ions intothe layer of anode active material 132, and contracts upon extraction ofcarrier ions from the layer of anode active material 132. The anodestructure backbone 134 may also include a top 1056 adjacent to the firstsecondary growth constraint 158, a bottom 1058 adjacent to the secondsecondary growth constraint 160, and a lateral surface (not marked)surrounding the vertical axis A_(ESB) and connecting the top 1056 andthe bottom 1058. The anode structure backbone 134 further includes alength L_(ESB), a width W_(ESB), and a height H_(ESB). The lengthL_(ESB) being bounded by the lateral surface and measured along the Xaxis. The width W_(ESB) being bounded by the lateral surface andmeasured along the Y axis, and the height H_(ESB) being measured alongthe Z axis from the top 1056 to the bottom 1058.

The L_(ESB) of the anode structure backbone 134 will vary depending uponthe energy storage device 100 or the secondary battery 102 and theirintended use(s). In general, however, the anode structure backbone 134will typically have a L_(ESB) in the range of about 5 mm to about 500mm. For example, in one such embodiment, the anode structure backbone134 will have a L_(ESB) of about 10 mm to about 250 mm. By way offurther example, in one such embodiment, the anode structure backbone134 will have a L_(ESB) of about 20 mm to about 100 mm. According to oneembodiment, the anode structure backbone 134 may be the substructure ofthe anode structure 110 that acts as the at least one connecting member166.

The W_(ESB) of the anode structure backbone 134 will also vary dependingupon the energy storage device 100 or the secondary battery 102 andtheir intended use(s). In general, however, each anode structurebackbone 134 will typically have a W_(ESB) of at least 1 micrometer. Forexample, in one embodiment, the W_(ESB) of each anode structure backbone134 may be substantially thicker, but generally will not have athickness in excess of 500 micrometers. By way of further example, inone embodiment, the W_(ESB) of each anode structure backbone 134 will bein the range of about 1 to about 50 micrometers.

The H_(ESB) of the anode structure backbone 134 will also vary dependingupon the energy storage device 100 or the secondary battery 102 andtheir intended use(s). In general, however, the anode structure backbone134 will typically have a H_(ESB) of at least about 50 micrometers, moretypically at least about 100 micrometers. Further, in general, the anodestructure backbone 134 will typically have a H_(ESB) of no more thanabout 10,000 micrometers, and more typically no more than about 5,000micrometers. For example, in one embodiment, the H_(ESB) of each anodestructure backbone 134 will be in the range of about 0.05 mm to about 10mm. By way of further example, in one embodiment, the H_(ESB) of eachanode structure backbone 134 will be in the range of about 0.05 mm toabout 5 mm. By way of further example, in one embodiment, the H_(ESB) ofeach anode structure backbone 134 will be in the range of about 0.1 mmto about 1 mm.

Depending upon the application, anode structure backbone 134 may beelectrically conductive or insulating. For example, in one embodiment,the anode structure backbone 134 may be electrically conductive and mayinclude anode current collector 136 for anode active material 132. Inone such embodiment, anode structure backbone 134 includes an anodecurrent collector 136 having a conductivity of at least about 10³Siemens/cm. By way of further example, in one such embodiment, anodestructure backbone 134 includes an anode current collector 136 having aconductivity of at least about 10⁴ Siemens/cm. By way of furtherexample, in one such embodiment, anode structure backbone 134 includesan anode current collector 136 having a conductivity of at least about10⁵ Siemens/cm. In other embodiments, anode structure backbone 134 isrelatively nonconductive. For example, in one embodiment, anodestructure backbone 134 has an electrical conductivity of less than 10Siemens/cm. By way of further example, in one embodiment, anodestructure backbone 134 has an electrical conductivity of less than 1Siemens/cm. By way of further example, in one embodiment, anodestructure backbone 134 has an electrical conductivity of less than 10⁻¹Siemens/cm.

In certain embodiments, anode structure backbone 134 may include anymaterial that may be shaped, such as metals, semiconductors, organics,ceramics, and glasses. For example, in certain embodiments, materialsinclude semiconductor materials such as silicon and germanium.Alternatively, however, carbon-based organic materials, or metals, suchas aluminum, copper, nickel, cobalt, titanium, and tungsten, may also beincorporated into anode structure backbone 134. In one exemplaryembodiment, anode structure backbone 134 comprises silicon. The silicon,for example, may be single crystal silicon, polycrystalline silicon,amorphous silicon, or a combination thereof.

In certain embodiments, the anode active material layer 132 may have athickness of at least one micrometer. Typically, however, the anodeactive material layer 132 thickness typically will not exceed 200micrometers. For example, in one embodiment, the anode active materiallayer 132 may have a thickness of about 1 to 50 micrometers. By way offurther example, in one embodiment, the anode active material layer 132may have a thickness of about 2 to about 75 micrometers. By way offurther example, in one embodiment, the anode active material layer 132may have a thickness of about 10 to about 100 micrometers. By way offurther example, in one embodiment, the anode active material layer 132may have a thickness of about 5 to about 50 micrometers.

In certain embodiments, the anode current collector 136 includes anionically permeable conductor material that has sufficient ionicpermeability to carrier ions to facilitate the movement of carrier ionsfrom the separator 130 to the anode active material layer 132, andsufficient electrical conductivity to enable it to serve as a currentcollector. Being positioned between the anode active material layer 132and the separator 130, the anode current collector 136 may facilitatemore uniform carrier ion transport by distributing current from theanode current collector 136 across the surface of the anode activematerial layer 132. This, in turn, may facilitate more uniform insertionand extraction of carrier ions and thereby reduce stress in the anodeactive material layer 132 during cycling; since the anode currentcollector 136 distributes current to the surface of the anode activematerial layer 132 facing the separator 130, the reactivity of the anodeactive material layer 132 for carrier ions will be the greatest wherethe carrier ion concentration is the greatest.

The anode current collector 136 includes an ionically permeableconductor material that is both ionically and electrically conductive.Stated differently, the anode current collector 136 has a thickness, anelectrical conductivity, and an ionic conductivity for carrier ions thatfacilitates the movement of carrier ions between an immediately adjacentanode active material layer 132 on one side of the ionically permeableconductor layer and an immediately adjacent separator layer 130 on theother side of the anode current collector 136 in an electrochemicalstack or electrode assembly 106. On a relative basis, the anode currentcollector 136 has an electrical conductance that is greater than itsionic conductance when there is an applied current to store energy inthe device 100 or an applied load to discharge the device 100. Forexample, the ratio of the electrical conductance to the ionicconductance (for carrier ions) of the anode current collector 136 willtypically be at least 1,000:1, respectively, when there is an appliedcurrent to store energy in the device 100 or an applied load todischarge the device 100. By way of further example, in one suchembodiment, the ratio of the electrical conductance to the ionicconductance (for carrier ions) of the anode current collector 136 is atleast 5,000:1, respectively, when there is an applied current to storeenergy in the device 100 or an applied load to discharge the device 100.By way of further example, in one such embodiment, the ratio of theelectrical conductance to the ionic conductance (for carrier ions) ofthe anode current collector 136 is at least 10,000:1, respectively, whenthere is an applied current to store energy in the device 100 or anapplied load to discharge the device 100. By way of further example, inone such embodiment, the ratio of the electrical conductance to theionic conductance (for carrier ions) of the anode current collector 136layer is at least 50,000:1, respectively, when there is an appliedcurrent to store energy in the device 100 or an applied load todischarge the device 100. By way of further example, in one suchembodiment, the ratio of the electrical conductance to the ionicconductance (for carrier ions) of the anode current collector 136 is atleast 100,000:1, respectively, when there is an applied current to storeenergy in the device 100 or an applied load to discharge the device 100.

In one embodiment, and when there is an applied current to store energyin the device 100 or an applied load to discharge the device 100, suchas when a secondary battery 102 is charging or discharging, the anodecurrent collector 136 has an ionic conductance that is comparable to theionic conductance of an adjacent separator layer 130. For example, inone embodiment, the anode current collector 136 has an ionic conductance(for carrier ions) that is at least 50% of the ionic conductance of theseparator layer 130 (i.e., a ratio of 0.5:1, respectively) when there isan applied current to store energy in the device 100 or an applied loadto discharge the device 100. By way of further example, in someembodiments, the ratio of the ionic conductance (for carrier ions) ofthe anode current collector 136 to the ionic conductance (for carrierions) of the separator layer 130 is at least 1:1 when there is anapplied current to store energy in the device 100 or an applied load todischarge the device 100. By way of further example, in someembodiments, the ratio of the ionic conductance (for carrier ions) ofthe anode current collector 136 to the ionic conductance (for carrierions) of the separator layer 130 is at least 1.25:1 when there is anapplied current to store energy in the device 100 or an applied load todischarge the device 100. By way of further example, in someembodiments, the ratio of the ionic conductance (for carrier ions) ofthe anode current collector 136 to the ionic conductance (for carrierions) of the separator layer 130 is at least 1.5:1 when there is anapplied current to store energy in the device 100 or an applied load todischarge the device 100. By way of further example, in someembodiments, the ratio of the ionic conductance (for carrier ions) ofthe anode current collector 136 to the ionic conductance (for carrierions) of the separator layer 130 is at least 2:1 when there is anapplied current to store energy in the device 100 or an applied load todischarge the device 100.

In one embodiment, the anode current collector 136 also has anelectrical conductance that is substantially greater than the electricalconductance of the anode active material layer 132. For example, in oneembodiment, the ratio of the electrical conductance of the anode currentcollector 136 to the electrical conductance of the anode active materiallayer 132 is at least 100:1 when there is an applied current to storeenergy in the device 100 or an applied load to discharge the device 100.By way of further example, in some embodiments, the ratio of theelectrical conductance of the anode current collector 136 to theelectrical conductance of the anode active material layer 132 is atleast 500:1 when there is an applied current to store energy in thedevice 100 or an applied load to discharge the device 100. By way offurther example, in some embodiments, the ratio of the electricalconductance of the anode current collector 136 to the electricalconductance of the anode active material layer 132 is at least 1000:1when there is an applied current to store energy in the device 100 or anapplied load to discharge the device 100. By way of further example, insome embodiments, the ratio of the electrical conductance of the anodecurrent collector 136 to the electrical conductance of the anode activematerial layer 132 is at least 5000:1 when there is an applied currentto store energy in the device 100 or an applied load to discharge thedevice 100. By way of further example, in some embodiments, the ratio ofthe electrical conductance of the anode current collector 136 to theelectrical conductance of the anode active material layer 132 is atleast 10,000:1 when there is an applied current to store energy in thedevice 100 or an applied load to discharge the device 100.

The thickness of the anode current collector layer 136 (i.e., theshortest distance between the separator 130 and, in one embodiment, theanodically active material layer between which the anode currentcollector layer 136 is sandwiched) in certain embodiments will dependupon the composition of the layer 136 and the performance specificationsfor the electrochemical stack. In general, when an anode currentcollector layer 136 is an ionically permeable conductor layer, it willhave a thickness of at least about 300 Angstroms. For example, in someembodiments, it may have a thickness in the range of about 300-800Angstroms. More typically, however, it will have a thickness greaterthan about 0.1 micrometers. In general, an ionically permeable conductorlayer will have a thickness not greater than about 100 micrometers.Thus, for example, in one embodiment, the electrode current collectorlayer 136 will have a thickness in the range of about 0.1 to about 10micrometers. By way of further example, in some embodiments, the anodecurrent collector layer 136 will have a thickness in the range of about0.1 to about 5 micrometers. By way of further example, in someembodiments, the anode current collector layer 136 will have a thicknessin the range of about 0.5 to about 3 micrometers. In general, it ispreferred that the thickness of the anode current collector layer 136 beapproximately uniform. For example, in one embodiment, it is preferredthat the anode current collector layer 136 have a thicknessnon-uniformity of less than about 25%. In certain embodiments, thethickness variation is even less. For example, in some embodiments, theanode current collector layer 136 has a thickness non-uniformity of lessthan about 20%. By way of further example, in some embodiments, theanode current collector layer 136 has a thickness non-uniformity of lessthan about 15%. In some embodiments the ionically permeable conductorlayer has a thickness non-uniformity of less than about 10%.

In one embodiment, the anode current collector layer 136 is an ionicallypermeable conductor layer including an electrically conductive componentand an ion conductive component that contribute to the ionicpermeability and electrical conductivity. Typically, the electricallyconductive component will include a continuous electrically conductivematerial (e.g., a continuous metal or metal alloy) in the form of a meshor patterned surface, a film, or composite material comprising thecontinuous electrically conductive material (e.g., a continuous metal ormetal alloy). Additionally, the ion conductive component will typicallycomprise pores, for example, interstices of a mesh, spaces between apatterned metal or metal alloy containing material layer, pores in ametal film, or a solid ion conductor having sufficient diffusivity forcarrier ions. In certain embodiments, the ionically permeable conductorlayer includes a deposited porous material, an ion-transportingmaterial, an ion-reactive material, a composite material, or aphysically porous material. If porous, for example, the ionicallypermeable conductor layer may have a void fraction of at least about0.25. In general, however, the void fraction will typically not exceedabout 0.95. More typically, when the ionically permeable conductor layeris porous the void fraction may be in the range of about 0.25 to about0.85. In some embodiments, for example, when the ionically permeableconductor layer is porous the void fraction may be in the range of about0.35 to about 0.65.

In the embodiment illustrated in FIG. 7, anode current collector layer136 is the sole anode current collector for electrode active materiallayer 132. Stated differently, anode structure backbone 134 may includean anode current collector. In certain other embodiments, however, anodestructure backbone 134 may optionally not include an anode currentcollector.

Population of Cathode Structures

Referring again to FIG. 7, each member of the population of cathodestructures 112 may also include a top 1068 adjacent to the firstsecondary growth constraint 158, a bottom 1070 adjacent to the secondsecondary growth constraint 160, and a lateral surface (not marked)surrounding a vertical axis A_(CES) (not marked) parallel to the Z axis,the lateral surface connecting the top 1068 and the bottom 1070. Thecathode structures 112 further include a length L_(C), a width W_(C),and a height H_(C). The length L_(C) being bounded by the lateralsurface and measured along the X axis. The width W_(C) being bounded bythe lateral surface and measured along the Y axis, and the height H_(C)being measured along the vertical axis A_(CES) or the Z axis from thetop 1068 to the bottom 1070.

The L_(C) of the members of the cathode population 112 will varydepending upon the energy storage device 100 or the secondary battery102 and their intended use(s). In general, however, the members of thecathode population 112 will typically have a L_(C) in the range of about5 mm to about 500 mm. For example, in one such embodiment, the membersof the cathode population 112 have a L_(C) of about 10 mm to about 250mm. By way of further example, in one such embodiment, the members ofthe cathode population 112 have a L_(C) of about 25 mm to about 100 mm.

The W_(C) of the members of the cathode population 112 will also varydepending upon the energy storage device 100 or the secondary battery102 and their intended use(s). In general, however, each member of thecathode population 112 will typically have a W_(C) within the range ofabout 0.01 mm to 2.5 mm. For example, in one embodiment, the W_(C) ofeach member of the cathode population 112 will be in the range of about0.025 mm to about 2 mm. By way of further example, in one embodiment,the W_(C) of each member of the cathode population 112 will be in therange of about 0.05 mm to about 1 mm.

The H_(C) of the members of the cathode population 112 will also varydepending upon the energy storage device 100 or the secondary battery102 and their intended use(s). In general, however, members of thecathode population 112 will typically have a H_(C) within the range ofabout 0.05 mm to about 10 mm. For example, in one embodiment, the H_(C)of each member of the cathode population 112 will be in the range ofabout 0.05 mm to about 5 mm. By way of further example, in oneembodiment, the H_(C) of each member of the cathode population 112 willbe in the range of about 0.1 mm to about 1 mm.

In another embodiment, each member of the population of cathodestructures 112 may include a cathode structure backbone 141 having avertical axis A_(CESB) parallel to the Z axis. The cathode structurebackbone 141 may also include a layer of cathode active material 138surrounding the cathode structure backbone 141 about the vertical axisA_(CESB). Stated alternatively, the cathode structure backbone 141provides mechanical stability for the layer of cathode active material138, and may provide a point of attachment for the primary growthconstraint system 151 and/or secondary growth constraint system 152. Thecathode structure backbone 141 may also include a top 1072 adjacent tothe first secondary growth constraint 158, a bottom 1074 adjacent to thesecond secondary growth constraint 160, and a lateral surface (notmarked) surrounding the vertical axis A_(CESB) and connecting the top1072 and the bottom 1074. The cathode structure backbone 141 furtherincludes a length L_(CESB), a width W_(CESB), and a height H_(CESB). Thelength L_(CESB) being bounded by the lateral surface and measured alongthe X axis. The width W_(CESB) being bounded by the lateral surface andmeasured along the Y axis, and the height H_(CESB) being measured alongthe Z axis from the top 1072 to the bottom 1074.

The L_(CESB) of the cathode structure backbone 141 will vary dependingupon the energy storage device 100 or the secondary battery 102 andtheir intended use(s). In general, however, the cathode structurebackbone 141 will typically have a L_(CESB) in the range of about 5 mmto about 500 mm. For example, in one such embodiment, the cathodestructure backbone 141 will have a L_(CESB) of about 10 mm to about 250mm. By way of further example, in one such embodiment, the cathodestructure backbone 141 will have a L_(CESB) of about 20 mm to about 100mm.

The W_(CESB) of the cathode structure backbone 141 will also varydepending upon the energy storage device 100 or the secondary battery102 and their intended use(s). In general, however, each cathodestructure backbone 141 will typically have a W_(CESB) of at least 1micrometer. For example, in one embodiment, the W_(CESB) of each cathodestructure backbone 141 may be substantially thicker, but generally willnot have a thickness in excess of 500 micrometers. By way of furtherexample, in one embodiment, the W_(CESB) of each cathode structurebackbone 141 will be in the range of about 1 to about 50 micrometers.

The H_(CESB) of the cathode structure backbone 141 will also varydepending upon the energy storage device 100 or the secondary battery102 and their intended use(s). In general, however, the cathodestructure backbone 141 will typically have a H_(CESB) of at least about50 micrometers, more typically at least about 100 micrometers. Further,in general, the cathode structure backbone 141 will typically have aH_(CESB) of no more than about 10,000 micrometers, and more typically nomore than about 5,000 micrometers. For example, in one embodiment, theH_(CESB) of each cathode structure backbone 141 will be in the range ofabout 0.05 mm to about 10 mm. By way of further example, in oneembodiment, the H_(CESB) of each cathode structure backbone 141 will bein the range of about 0.05 mm to about 5 mm. By way of further example,in one embodiment, the H_(CESB) of each cathode structure backbone 141will be in the range of about 0.1 mm to about 1 mm.

Depending upon the application, cathode structure backbone 141 may beelectrically conductive or insulating. For example, in one embodiment,the cathode structure backbone 141 may be electrically conductive andmay include cathode current collector 140 for cathode active material138. In one such embodiment, cathode structure backbone 141 includes acathode current collector 140 having a conductivity of at least about10³ Siemens/cm. By way of further example, in one such embodiment,cathode structure backbone 141 includes a cathode current collector 140having a conductivity of at least about 10⁴ Siemens/cm. By way offurther example, in one such embodiment, cathode structure backbone 141includes a cathode current collector 140 having a conductivity of atleast about 10⁵ Siemens/cm. In other embodiments, cathode structurebackbone 141 is relatively nonconductive. For example, in oneembodiment, cathode structure backbone 141 has an electricalconductivity of less than 10 Siemens/cm. By way of further example, inone embodiment, cathode structure backbone 141 has an electricalconductivity of less than 1 Siemens/cm. By way of further example, inone embodiment, cathode structure backbone 141 has an electricalconductivity of less than 10⁻¹ Siemens/cm.

In certain embodiments, cathode structure backbone 141 may include anymaterial that may be shaped, such as metals, semiconductors, organics,ceramics, and glasses. For example, in certain embodiments, materialsinclude semiconductor materials such as silicon and germanium.Alternatively, however, carbon-based organic materials, or metals, suchas aluminum, copper, nickel, cobalt, titanium, and tungsten, may also beincorporated into cathode structure backbone 141. In one exemplaryembodiment, cathode structure backbone 141 comprises silicon. Thesilicon, for example, may be single crystal silicon, polycrystallinesilicon, amorphous silicon, or a combination thereof.

In certain embodiments, the cathode active material layer 138 may have athickness of at least one micrometer. Typically, however, the cathodeactive material layer 138 thickness will not exceed 200 micrometers. Forexample, in one embodiment, the cathode active material layer 138 mayhave a thickness of about 1 to 50 micrometers. By way of furtherexample, in one embodiment, the cathode active material layer 138 mayhave a thickness of about 2 to about 75 micrometers. By way of furtherexample, in one embodiment, the cathode active material layer 138 mayhave a thickness of about 10 to about 100 micrometers. By way of furtherexample, in one embodiment, the cathode active material layer 138 mayhave a thickness of about 5 to about 50 micrometers.

In certain embodiments, the cathode current collector 140 includes anionically permeable conductor that has sufficient ionic permeability tocarrier ions to facilitate the movement of carrier ions from theseparator 130 to the cathode active material layer 138, and sufficientelectrical conductivity to enable it to serve as a current collector.Whether or not positioned between the cathode active material layer 138and the separator 130, the cathode current collector 140 may facilitatemore uniform carrier ion transport by distributing current from thecathode current collector 140 across the surface of the cathode activematerial layer 138. This, in turn, may facilitate more uniform insertionand extraction of carrier ions and thereby reduce stress in the cathodeactive material layer 138 during cycling; since the cathode currentcollector 140 distributes current to the surface of the cathode activematerial layer 138 facing the separator 130, the reactivity of thecathode active material layer 138 for carrier ions will be the greatestwhere the carrier ion concentration is the greatest.

The cathode current collector 140 includes an ionically permeableconductor material that is both ionically and electrically conductive.Stated differently, the cathode current collector 140 has a thickness,an electrical conductivity, and an ionic conductivity for carrier ionsthat facilitates the movement of carrier ions between an immediatelyadjacent cathode active material layer 138 on one side of the ionicallypermeable conductor layer and an immediately adjacent separator layer130 on the other side of the cathode current collector 140 in anelectrochemical stack or electrode assembly 106. On a relative basis,the cathode current collector 140 has an electrical conductance that isgreater than its ionic conductance when there is an applied current tostore energy in the device 100 or an applied load to discharge thedevice 100. For example, the ratio of the electrical conductance to theionic conductance (for carrier ions) of the cathode current collector140 will typically be at least 1,000:1, respectively, when there is anapplied current to store energy in the device 100 or an applied load todischarge the device 100. By way of further example, in one suchembodiment, the ratio of the electrical conductance to the ionicconductance (for carrier ions) of the cathode current collector 140 isat least 5,000:1, respectively, when there is an applied current tostore energy in the device 100 or an applied load to discharge thedevice 100. By way of further example, in one such embodiment, the ratioof the electrical conductance to the ionic conductance (for carrierions) of the cathode current collector 140 is at least 10,000:1,respectively, when there is an applied current to store energy in thedevice 100 or an applied load to discharge the device 100. By way offurther example, in one such embodiment, the ratio of the electricalconductance to the ionic conductance (for carrier ions) of the cathodecurrent collector 140 layer is at least 50,000:1, respectively, whenthere is an applied current to store energy in the device 100 or anapplied load to discharge the device 100. By way of further example, inone such embodiment, the ratio of the electrical conductance to theionic conductance (for carrier ions) of the cathode current collector140 is at least 100,000:1, respectively, when there is an appliedcurrent to store energy in the device 100 or an applied load todischarge the device 100.

In one embodiment, and when there is an applied current to store energyin the device 100 or an applied load to discharge the device 100, suchas when an energy storage device 100 or a secondary battery 102 ischarging or discharging, the cathode current collector 140 has an ionicconductance that is comparable to the ionic conductance of an adjacentseparator layer 130. For example, in one embodiment, the cathode currentcollector 140 has an ionic conductance (for carrier ions) that is atleast 50% of the ionic conductance of the separator layer 130 (i.e., aratio of 0.5:1, respectively) when there is an applied current to storeenergy in the device 100 or an applied load to discharge the device 100.By way of further example, in some embodiments, the ratio of the ionicconductance (for carrier ions) of the cathode current collector 140 tothe ionic conductance (for carrier ions) of the separator layer 130 isat least 1:1 when there is an applied current to store energy in thedevice 100 or an applied load to discharge the device 100. By way offurther example, in some embodiments, the ratio of the ionic conductance(for carrier ions) of the cathode current collector 140 to the ionicconductance (for carrier ions) of the separator layer 130 is at least1.25:1 when there is an applied current to store energy in the device100 or an applied load to discharge the device 100. By way of furtherexample, in some embodiments, the ratio of the ionic conductance (forcarrier ions) of the cathode current collector 140 to the ionicconductance (for carrier ions) of the separator layer 130 is at least1.5:1 when there is an applied current to store energy in the device 100or an applied load to discharge the device 100. By way of furtherexample, in some embodiments, the ratio of the ionic conductance (forcarrier ions) of the cathode current collector 140 to the ionicconductance (for (anode current collector layer) carrier ions) of theseparator layer 130 is at least 2:1 when there is an applied current tostore energy in the device 100 or an applied load to discharge thedevice 100.

In one embodiment, the cathode current collector 140 also has anelectrical conductance that is substantially greater than the electricalconductance of the cathode active material layer 138. For example, inone embodiment, the ratio of the electrical conductance of the cathodecurrent collector 140 to the electrical conductance of the cathodeactive material layer 138 is at least 100:1 when there is an appliedcurrent to store energy in the device 100 or an applied load todischarge the device 100. By way of further example, in someembodiments, the ratio of the electrical conductance of the cathodecurrent collector 140 to the electrical conductance of the cathodeactive material layer 138 is at least 500:1 when there is an appliedcurrent to store energy in the device 100 or an applied load todischarge the device 100. By way of further example, in someembodiments, the ratio of the electrical conductance of the cathodecurrent collector 140 to the electrical conductance of the cathodeactive material layer 138 is at least 1000:1 when there is an appliedcurrent to store energy in the device 100 or an applied load todischarge the device 100. By way of further example, in someembodiments, the ratio of the electrical conductance of the cathodecurrent collector 140 to the electrical conductance of the cathodeactive material layer 138 is at least 5000:1 when there is an appliedcurrent to store energy in the device 100 or an applied load todischarge the device 100. By way of further example, in someembodiments, the ratio of the electrical conductance of the cathodecurrent collector 140 to the electrical conductance of the cathodeactive material layer 138 is at least 10,000:1 when there is an appliedcurrent to store energy in the device 100 or an applied load todischarge the device 100.

The thickness of the cathode current collector layer 140 (i.e., theshortest distance between the separator 130 and, in one embodiment, thecathodic active material layer 138 between which the cathode currentcollector layer 140 is sandwiched) in certain embodiments will dependupon the composition of the layer 140 and the performance specificationsfor the electrochemical stack. In general, when an cathode currentcollector layer 140 is an ionically permeable conductor layer, it willhave a thickness of at least about 300 Angstroms. For example, in someembodiments, it may have a thickness in the range of about 300-800Angstroms. More typically, however, it will have a thickness greaterthan about 0.1 micrometers. In general, an ionically permeable conductorlayer will have a thickness not greater than about 100 micrometers.Thus, for example, in one embodiment, the cathode current collectorlayer 140 will have a thickness in the range of about 0.1 to about 10micrometers. By way of further example, in some embodiments, the cathodecurrent collector layer 140 will have a thickness in the range of about0.1 to about 5 micrometers. By way of further example, in someembodiments, the cathode current collector layer 140 will have athickness in the range of about 0.5 to about 3 micrometers. In general,it is preferred that the thickness of the cathode current collectorlayer 140 be approximately uniform. For example, in one embodiment, itis preferred that the cathode current collector layer 140 have athickness non-uniformity of less than about 25%. In certain embodiments,the thickness variation is even less. For example, in some embodiments,the cathode current collector layer 140 has a thickness non-uniformityof less than about 20%. By way of further example, in some embodiments,the cathode current collector layer 140 has a thickness non-uniformityof less than about 15%. In some embodiments, the cathode currentcollector layer 140 has a thickness non-uniformity of less than about10%.

In one embodiment, the cathode current collector layer 140 is anionically permeable conductor layer including an electrically conductivecomponent and an ion conductive component that contributes to the ionicpermeability and electrical conductivity. Typically, the electricallyconductive component will include a continuous electrically conductivematerial (e.g., a continuous metal or metal alloy) in the form of a meshor patterned surface, a film, or composite material comprising thecontinuous electrically conductive material (e.g., a continuous metal ormetal alloy). Additionally, the ion conductive component will typicallycomprise pores, for example, interstices of a mesh, spaces between apatterned metal or metal alloy containing material layer, pores in ametal film, or a solid ion conductor having sufficient diffusivity forcarrier ions. In certain embodiments, the ionically permeable conductorlayer includes a deposited porous material, an ion-transportingmaterial, an ion-reactive material, a composite material, or aphysically porous material. If porous, for example, the ionicallypermeable conductor layer may have a void fraction of at least about0.25. In general, however, the void fraction will typically not exceedabout 0.95. More typically, when the ionically permeable conductor layeris porous the void fraction may be in the range of about 0.25 to about0.85. In some embodiments, for example, when the ionically permeableconductor layer is porous the void fraction may be in the range of about0.35 to about 0.65.

In the embodiment illustrated in FIG. 7, cathode current collector layer140 is the sole cathode current collector for cathode active materiallayer 138. Stated differently, cathode structure backbone 141 mayinclude a cathode current collector 140. In certain other embodiments,however, cathode structure backbone 141 may optionally not include acathode current collector 140.

In one embodiment, first secondary growth constraint 158 and secondsecondary growth constraint 160 each may include an inner surface 1060and 1062, respectively, and an opposing outer surface 1064 and 1066,respectively, separated along the z-axis thereby defining a firstsecondary growth constraint 158 height H₁₅₈ and a second secondarygrowth constraint 160 height H₁₆₀. According to aspects of thedisclosure, increasing the heights of either the first and/or secondsecondary growth constraints 158, 160, respectively, can increase thestiffness of the constraints, but can also require increased volume,thus causing a reduction in energy density for an energy storage device100 or a secondary battery 102 containing the electrode assembly 106 andset of constraints 108. Accordingly, the thickness of the constraints158, 160 can be selected in accordance with the constraint materialproperties, the strength of the constraint required to offset pressurefrom a predetermined expansion of an electrode 100, and other factors.For example, in one embodiment, the first and second secondary growthconstraint heights H₁₅₈ and H₁₆₀, respectively, may be less than 50% ofthe height H_(ES). By way of further example, in one embodiment, thefirst and second secondary growth constraint heights H₁₅₈ and H₁₆₀,respectively, may be less than 25% of the height H_(ES). By way offurther example, in one embodiment, the first and second secondarygrowth constraint heights H₁₅₈ and H₁₆₀, respectively, may be less than10% of the height H_(ES). By way of further example, in one embodiment,the first and second secondary growth constraint heights H₁₅₈ and H₁₆₀may be may be less than about 5% of the height H_(ES). In someembodiments, the first secondary growth constraint height H₁₅₈ and thesecond secondary growth constraint height H₁₆₀ may be different, and thematerials used for each of the first and second secondary growthconstraints 158, 160 may also be different.

In certain embodiments, the inner surfaces 1060 and 1062 may includesurface features amenable to affixing the population of anode structures110 and/or the population of cathode structures 112 thereto, and theouter surfaces 1064 and 1066 may include surface features amenable tothe stacking of a plurality of constrained electrode assemblies 106(i.e., inferred within FIG. 7, but not shown for clarity). For example,in one embodiment, the inner surfaces 1060 and 1062 or the outersurfaces 1064 and 1066 may be planar. By way of further example, in oneembodiment, the inner surfaces 1060 and 1062 or the outer surfaces 1064and 1066 may be non-planar. By way of further example, in oneembodiment, the inner surfaces 1060 and 1062 and the outer surfaces 1064and 1066 may be planar. By way of further example, in one embodiment,the inner surfaces 1060 and 1062 and the outer surfaces 1064 and 1066may be non-planar. By way of further example, in one embodiment, theinner surfaces 1060 and 1062 and the outer surfaces 1064 and 1066 may besubstantially planar.

As described elsewhere herein, modes for affixing the at least onesecondary connecting member 166 embodied as anode structures 110 and/orcathode structures 112 to the inner surfaces 1060 and 1062 may varydepending upon the energy storage device 100 or secondary battery 102and their intended use(s). As one exemplary embodiment shown in FIG. 7,the top 1052 and the bottom 1054 of the population of anode structures110 (i.e., anode current collector 136, as shown) and the top 1068 andbottom 1070 of the population of cathode structures 112 (i.e., cathodecurrent collector 140, as shown) may be affixed to the inner surface1060 of the first secondary growth constraint 158 and the inner surface1062 of the second secondary growth constraint 160 via a layer of glue182. Alternatively, in certain embodiments only the anode currentcollectors 136, or only the cathode current collectors 140, may beaffixed to serve as the at least one secondary connecting member 166, oranother sub-structure of the anode and/or cathode structures may serveas the at least one secondary connecting member 166. Similarly, a top1076 and a bottom 1078 of the first primary growth constraint 154, and atop 1080 and a bottom 1082 of the second primary growth constraint 156may be affixed to the inner surface 1060 of the first secondary growthconstraint 158 and the inner surface 1062 of the second secondary growthconstraint 160 via a layer of glue 182.

Stated alternatively, in the embodiment shown in FIG. 7, the top 1052and the bottom 1054 of the population of anode structures 110 include aheight H_(ES) that effectively meets both the inner surface 1060 of thefirst secondary growth constraint 158 and the inner surface 1062 of thesecond secondary growth constraint 160, and may be affixed to the innersurface 1060 of the first secondary growth constraint 158 and the innersurface 1062 of the second secondary growth constraint 160 via a layerof glue 182 in a flush embodiment. In addition, the top 1068 and thebottom 1070 of the population of cathode structures 112 include a heightH_(CES) that effectively meets both the inner surface 1060 of the firstsecondary growth constraint 158 and the inner surface 1062 of the secondsecondary growth constraint 160, and may be affixed to the inner surface1060 of the first secondary growth constraint 158 and the inner surface1062 of the second secondary growth constraint 160 via a layer of glue182 in a flush embodiment.

Further, in another exemplary embodiment, a top 1056 and a bottom 1058of the anode backbones 134, and a top 1072 and a bottom 1074 of thecathode backbones 141 may be affixed to the inner surface 1060 of thefirst secondary growth constraint 158 and the inner surface 1062 of thesecond secondary growth constraint 160 via a layer of glue 182 (notillustrated). Similarly, a top 1076 and a bottom 1078 of the firstprimary growth constraint 154, and a top 1080 and a bottom 1082 of thesecond primary growth constraint 156 may be affixed to the inner surface1060 of the first secondary growth constraint 158 and the inner surface1062 of the second secondary growth constraint 160 via a layer of glue182 (not illustrated with respect to the embodiment described in thisparagraph). Stated alternatively, the top 1056 and the bottom 1058 ofthe anode backbones 134 include a height H_(ESB) that effectively meetsboth the inner surface 1060 of the first secondary growth constraint 158and the inner surface 1062 of the second secondary growth constraint160, and may be affixed to the inner surface 1060 of the first secondarygrowth constraint 158 and the inner surface 1062 of the second secondarygrowth constraint 160 via a layer of glue 182 in a flush embodiment. Inaddition, the top 1072 and the bottom 1074 of the cathode backbones 141include a height H_(CESB) that effectively meets both the inner surface1060 of the first secondary growth constraint 158 and the inner surface1062 of the second secondary growth constraint 160, and may be affixedto the inner surface 1060 of the first secondary growth constraint 158and the inner surface 1062 of the second secondary growth constraint 160via a layer of glue 182 in a flush embodiment.

Accordingly, in one embodiment, at least a portion of the population ofanode 110 and/or cathode structures 112, and/or the separator 130 mayserve as one or more secondary connecting members 166 to connect thefirst and second secondary growth constraints 158, 160, respectively, toone another in a secondary growth constraint system 152, therebyproviding a compact and space-efficient constraint system to restraingrowth of the electrode assembly 106 during cycling thereof. Accordingto one embodiment, any portion of the anode 110 and/or cathodestructures 112, and/or separator 130 may serve as the one or moresecondary connecting members 166, with the exception of any portion ofthe anode 110 and/or cathode structure 112 that swells in volume withcharge and discharge cycles. That is, that portion of the anode 110and/or cathode structure 112, such as the anode active material 132,that is the cause of the volume change in the electrode assembly 106,typically will not serve as a part of the set of electrode constraints108. In one embodiment, first and second primary growth constraints 154,156, respectively, provided as a part of the primary growth constraintsystem 151 further inhibit growth in a longitudinal direction, and mayalso serve as secondary connecting members 166 to connect the first andsecond secondary growth constraints 158, 160, respectively, of thesecondary growth constraint system 152, thereby providing a cooperative,synergistic constraint system (i.e., set of electrode constraints 108)for restraint of anode growth/swelling.

Secondary Battery

Referring now to FIG. 9, illustrated is an exploded view of oneembodiment of a secondary battery 102. The secondary battery 102includes battery enclosure 104 and a set of electrode assemblies 106 awithin the battery enclosure 104, each of the electrode assemblies 106having a first longitudinal end surface 116, an opposing secondlongitudinal end surface 118 (i.e., separated from first longitudinalend surface 116 along the Y axis the Cartesian coordinate system shown),as described above. Each electrode assembly 106 includes a population ofanode structures 110 and a population of cathode structures 112, stackedrelative to each other within each of the electrode assemblies 106 in astacking direction D; stated differently, the populations of anode 110and cathode 112 structures are arranged in an alternating series ofanodes 110 and cathodes 112 with the series progressing in the stackingdirection D between first and second longitudinal end surfaces 116, 118,respectively (see, e.g., FIG. 2; as illustrated in FIG. 2 and FIG. 9,stacking direction D parallels the Y axis of the Cartesian coordinatesystem(s) shown), as described above. In addition, the stackingdirection D within an individual electrode assembly 106 is perpendicularto the direction of stacking of a collection of electrode assemblies 106within a set 106 a (i.e., an electrode assembly stacking direction);stated differently, the electrode assemblies 106 are disposed relativeto each other in a direction within a set 106 a that is perpendicular tothe stacking direction D within an individual electrode assembly 106(e.g., the electrode assembly stacking direction is in a directioncorresponding to the Z axis of the Cartesian coordinate system shown,whereas the stacking direction D within individual electrode assemblies106 is in a direction corresponding to the Y axis of the Cartesiancoordinate system shown).

While the set of electrode assemblies 106 a depicted in the embodimentshown in FIG. 9 contains individual electrode assemblies 106 having thesame general size, one or more of the individual electrode assemblies106 may also and/or alternatively have different sizes in at least onedimension thereof, than the other electrode assemblies 106 in the set106 a. For example, according to one embodiment, the electrodeassemblies 106 that are stacked together to form the set 106 a providedin the secondary battery 102 may have different maximum widths W_(EA) inthe longitudinal direction (i.e., stacking direction D) of each assembly106. According to another embodiment, the electrode assemblies 106making up the stacked set 106 a provided in the secondary battery 102may have different maximum lengths L_(EA) along the transverse axis thatis orthogonal to the longitudinal axis. By way of further example, inone embodiment, each electrode assembly 106 that is stacked together toform the set of electrode assemblies 106 a in the secondary battery 102has a maximum width W_(EA) along the longitudinal axis and a maximumlength L_(EA) along the transverse axis that is selected to provide anarea of L_(EA)×W_(EA) that decreases along a direction in which theelectrode assemblies 106 are stacked together to form the set ofelectrode assemblies 106 a. For example, the maximum width W_(EA) andmaximum length L_(EA) of each electrode assembly 106 may be selected tobe less than that of an electrode assembly 106 adjacent thereto in afirst direction in which the assemblies 106 are stacked, and to begreater than that of an electrode assembly 106 adjacent thereto in asecond direction that is opposite thereto, such that the electrodeassemblies 106 are stacked together to form a secondary battery 102having a set of electrode assemblies 106 a in a pyramidal shape.Alternatively, the maximum lengths L_(EA) and maximum widths W_(EA) foreach electrode assembly 106 can be selected to provide different shapesand/or configurations for the stacked electrode assembly set 106 a. Themaximum vertical height H_(EA) for one or more of the electrodeassemblies 106 can also and/or alternatively be selected to be differentfrom other assemblies 106 in the set 106 a and/or to provide a stackedset 106 a having a predetermined shape and/or configuration.

Tabs 190, 192 project out of the battery enclosure 104 and provide anelectrical connection between the electrode assemblies 106 of set 106 aand an energy supply or consumer (not shown). More specifically, in thisembodiment tab 190 is electrically connected to tab extension 191 (e.g.,using an electrically conductive glue), and tab extension 191 iselectrically connected to the electrodes 110 comprised by each of theelectrode assemblies 106. Similarly, tab 192 is electrically connectedto tab extension 193 (e.g., using an electrically conductive glue), andtab extension 193 is electrically connected to the counter-electrodes112 comprised by each of electrode assemblies 106.

Each electrode assembly 106 in the embodiment illustrated in FIG. 9 mayhave an associated primary growth constraint system 151 to restraingrowth in the longitudinal direction (i.e., stacking direction D).Alternatively, in one embodiment, a plurality of electrode assemblies106 making up a set 106 a may share at least a portion of the primarygrowth constraint system 151. In the embodiment as shown, each primarygrowth constraint system 151 includes first and second primary growthconstraints 154, 156, respectively, that may overlie first and secondlongitudinal end surfaces 116, 118, respectively, as described above;and first and second opposing primary connecting members 162, 164,respectively, that may overlie lateral surfaces 142, as described above.First and second opposing primary connecting members 162, 164,respectively, may pull first and second primary growth constraints 154,156, respectively, towards each other, or alternatively stated, assistin restraining growth of the electrode assembly 106 in the longitudinaldirection, and primary growth constraints 154, 156 may apply acompressive or restraint force to the opposing first and secondlongitudinal end surfaces 116, 118, respectively. As a result, expansionof the electrode assembly 106 in the longitudinal direction is inhibitedduring formation and/or cycling of the battery 102 between charged anddischarged states. Additionally, primary growth constraint system 151exerts a pressure on the electrode assembly 106 in the longitudinaldirection (i.e., stacking direction D) that exceeds the pressuremaintained on the electrode assembly 106 in either of the two directionsthat are mutually perpendicular to each other and are perpendicular tothe longitudinal direction (e.g., as illustrated, the longitudinaldirection corresponds to the direction of the Y axis, and the twodirections that are mutually perpendicular to each other and to thelongitudinal direction correspond to the directions of the X axis andthe Z axis, respectively, of the illustrated Cartesian coordinatesystem).

Further, each electrode assembly 106 in the embodiment illustrated inFIG. 9 has an associated secondary growth constraint system 152 torestrain growth in the vertical direction (i.e., expansion of theelectrode assembly 106, anodes 110, and/or cathodes 112 in the verticaldirection (i.e., along the Z axis of the Cartesian coordinate system)).Alternatively, in one embodiment, a plurality of electrode assemblies106 making up a set 106 a share at least a portion of the secondarygrowth constraint system 152. Each secondary growth constraint system152 includes first and second secondary growth constraints 158, 160,respectively, that may overlie corresponding lateral surfaces 142,respectively, and at least one secondary connecting member 166, each asdescribed in more detail above. Secondary connecting members 166 maypull first and second secondary growth constraints 158, 160,respectively, towards each other, or alternatively stated, assist inrestraining growth of the electrode assembly 106 in the verticaldirection, and first and second secondary growth constraints 158, 160,respectively, may apply a compressive or restraint force to the lateralsurfaces 142), each as described above in more detail. As a result,expansion of the electrode assembly 106 in the vertical direction isinhibited during formation and/or cycling of the battery 102 betweencharged and discharged states. Additionally, secondary growth constraintsystem 152 exerts a pressure on the electrode assembly 106 in thevertical direction (i.e., parallel to the Z axis of the Cartesiancoordinate system) that exceeds the pressure maintained on the electrodeassembly 106 in either of the two directions that are mutuallyperpendicular to each other and are perpendicular to the verticaldirection (e.g., as illustrated, the vertical direction corresponds tothe direction of the Z axis, and the two directions that are mutuallyperpendicular to each other and to the vertical direction correspond tothe directions of the X axis and the Y axis, respectively, of theillustrated Cartesian coordinate system).

Further still, each electrode assembly 106 in the embodiment illustratedin FIG. 9 may have an associated primary growth constraint system151—and an associated secondary growth constraint system 152—to restraingrowth in the longitudinal direction and the vertical direction, asdescribed in more detail above. Furthermore, according to certainembodiments, the anode and/or cathode tabs 190, 192, respectively, andtab extensions 191, 193 can serve as a part of the tertiary growthconstraint system 155. For example, in certain embodiments, the tabextensions 191, 193 may extend along the opposing transverse surfaceregions 144, 146 to act as a part of the tertiary constraint system 155,such as the first and second tertiary growth constraints 157, 159. Thetab extensions 191, 193 can be connected to the primary growthconstraints 154, 156 at the longitudinal ends 117, 119 of the electrodeassembly 106, such that the primary growth constraints 154, 156 serve asthe at least one tertiary connecting member 165 that places the tabextensions 191, 193 in tension with one another to compress theelectrode assembly 106 along the transverse direction, and act as firstand second tertiary growth constraints 157, 159, respectively.Conversely, the tabs 190, 192 and/or tab extensions 191, 193 can alsoserve as the first and second primary connecting members 162, 164,respectively, for the first and second primary growth constraints 154,156, respectively, according to one embodiment. In yet anotherembodiment, the tabs 190, 192 and/or tab extensions 191, 193 can serveas a part of the secondary growth constraint system 152, such as byforming a part of the at least one secondary connecting member 166connecting the secondary growth constraints 158, 160. Accordingly, thetabs 190, 192 and/or tab extensions 191, 193 can assist in restrainingoverall macroscopic growth of the electrode assembly 106 by eitherserving as a part of one or more of the primary and secondary constraintsystems 151, 152, respectively, and/or by forming a part of a tertiarygrowth constraint system 155 to constrain the electrode assembly 106 ina direction orthogonal to the direction being constrained by one or moreof the primary and secondary growth constraint systems 151, 152,respectively.

To complete the assembly of the secondary battery 102, battery enclosure104 is filled with a non-aqueous electrolyte (not shown) and lid 104 ais folded over (along fold line, FL) and sealed to upper surface 104 b.When fully assembled, the sealed secondary battery 102 occupies a volumebounded by its exterior surfaces (i.e., the displacement volume), thesecondary battery enclosure 104 occupies a volume corresponding to thedisplacement volume of the battery (including lid 104 a) less itsinterior volume (i.e., the prismatic volume bounded by interior surfaces104 c, 104 d, 104 e, 104 f, 104 g and lid 104 a) and each growthconstraint 151, 152 of set 106 a occupies a volume corresponding to itsrespective displacement volume. In combination, therefore, the batteryenclosure 104 and growth constraints 151, 152 occupy no more than 75% ofthe volume bounded by the outer surface of the battery enclosure 104(i.e., the displacement volume of the battery). For example, in one suchembodiment, the growth constraints 151, 152 and battery enclosure 104,in combination, occupy no more than 60% of the volume bounded by theouter surface of the battery enclosure 104. By way of further example,in one such embodiment, the constraints 151, 152 and battery enclosure104, in combination, occupy no more than 45% of the volume bounded bythe outer surface of the battery enclosure 104. By way of furtherexample, in one such embodiment, the constraints 151, 152 and batteryenclosure 104, in combination, occupy no more than 30% of the volumebounded by the outer surface of the battery enclosure 104. By way offurther example, in one such embodiment, the constraints 151, 152 andbattery enclosure 104, in combination, occupy no more than 20% of thevolume bounded by the outer surface of the battery enclosure.

For ease of illustration in FIG. 9, secondary battery 102 includes onlyone set 106 a of electrode assemblies 106 and the set 106 a includesonly six electrode assemblies 106. In practice, the secondary battery102 may include more than one set of electrode assemblies 106 a, witheach of the sets 106 a being disposed laterally relative to each other(e.g., in a relative direction lying within the X-Y plane of theCartesian coordinate system of FIG. 9) or vertically relative to eachother (e.g., in a direction substantially parallel to the Z axis of theCartesian coordinate system of FIG. 9). Additionally, in each of theseembodiments, each of the sets of electrode assemblies 106 a may includeone or more electrode assemblies 106. For example, in certainembodiments, the secondary battery 102 may comprise one, two, or moresets of electrode assemblies 106 a, with each such set 106 a includingone or more electrode assemblies 106 (e.g., 1, 2, 3, 4, 5, 6, 10, 15, ormore electrode assemblies 106 within each such set 106 a) and, when thebattery 102 includes two or more such sets 106 a, the sets 106 a may belaterally or vertically disposed relative to other sets of electrodeassemblies 106 a included in the secondary battery 102. In each of thesevarious embodiments, each individual electrode assembly 106 may have itsown growth constraint(s), as described above (i.e., a 1:1 relationshipbetween electrode assemblies 106 and constraints 151, 152), two moreelectrode assemblies 106 may have a common growth constraint(s) 151,152, as described above (i.e., a set of constraints 108 for two or moreelectrode assemblies 106), or two or more electrode assemblies 106 mayshare components of a growth constraint(s) 151, 152 (i.e., two or moreelectrode assemblies 106 may have a common compression member (e.g.,second secondary growth constraint 158) and/or tension members 166, forexample, as in the fused embodiment, as described above).

Other Battery Components

In certain embodiments, the set of electrode constraints 108, includinga primary growth constraint system 151 and a secondary growth constraintsystem 152, as described above, may be derived from a sheet 2000 havinga length L₁, width W₁, and thickness t₁, as shown for example in FIG. 9.More specifically, to form a primary growth constraint system 151, asheet 2000 may be wrapped around an electrode assembly 106 and folded atfolded at edges 2001 to enclose the electrode assembly 106.Alternatively, in one embodiment, the sheet 2000 may be wrapped around aplurality of electrode assemblies 106 that are stacked to form anelectrode assembly set 106 a. The edges of the sheet may overlap eachother, and are welded, glued, or otherwise secured to each other to forma primary growth constraint system 151 including first primary growthconstraint 154 and second primary growth constraint 156, and firstprimary connecting member 162 and second primary connecting member 164.In this embodiment, the primary growth constraint system 151 has avolume corresponding to the displacement volume of sheet 2000 (i.e., themultiplication product of L₁, W₁ and t₁). In one embodiment, the atleast one primary connecting member is stretched in the stackingdirection D to place the member in tension, which causes a compressiveforce to be exerted by the first and second primary growth constraints.Alternatively, the at least one secondary connecting member can bestretched in the second direction to place the member in tension, whichcauses a compressive force to be exerted by the first and secondsecondary growth constraints. In an alternative embodiment, instead ofstretching the connecting members to place them in tension, theconnecting members and/or growth constraints or other portion of one ormore of the primary and secondary growth constraint systems may bepre-tensioned prior to installation over and/or in the electrodeassembly. In another alternative embodiment, the connecting membersand/or growth constraints and/or other portions of one or more of theprimary and secondary growth constraint systems are not initially undertension at the time of installation into and/or over the electrodeassembly, but rather, formation of the battery causes the electrodeassembly to expand and induce tension in portions of the primary and/orsecondary growth constraint systems such as the connecting membersand/or growth constraints. (i.e., self-tensioning).

Sheet 2000 may comprise any of a wide range of compatible materialscapable of applying the desired force to the electrode assembly 106. Ingeneral, the primary growth constraint system 151 will typicallycomprise a material that has an ultimate tensile strength of at least10,000 psi (>70 MPa), that is compatible with the battery electrolyte,does not significantly corrode at the floating or anode potential forthe battery 102, and does not significantly react or lose mechanicalstrength at 45° C., and even up to 70° C. For example, the primarygrowth constraint system 151 may comprise any of a wide range of metals,alloys, ceramics, glass, plastics, or a combination thereof (i.e., acomposite). In one exemplary embodiment, primary growth constraintsystem 151 comprises a metal such as stainless steel (e.g., SS 316, 440Cor 440C hard), aluminum (e.g., aluminum 7075-T6, hard H18), titanium(e.g., 6AI-4V), beryllium, beryllium copper (hard), copper (O₂ free,hard), nickel; in general, however, when the primary growth constraintsystem 151 comprises metal it is generally preferred that it beincorporated in a manner that limits corrosion and limits creating anelectrical short between the anodes 110 and cathodes 112. In anotherexemplary embodiment, the primary growth constraint system 151 comprisesa ceramic such as alumina (e.g., sintered or Coorstek AD96), zirconia(e.g., Coorstek YZTP), yttria-stabilized zirconia (e.g., ENrGE-Strate®). In another exemplary embodiment, the primary growthconstraint system 151 comprises a glass such as Schott D263 temperedglass. In another exemplary embodiment, the primary growth constraintsystem 151 comprises a plastic such as polyetheretherketone (PEEK)(e.g., Aptiv 1102), PEEK with carbon (e.g., Victrex 90HMF40 or Xycomp1000-04), polyphenylene sulfide (PPS) with carbon (e.g., Tepex Dynalite207), polyetheretherketone (PEEK) with 30% glass, (e.g., Victrex 90HMF40or Xycomp 1000-04), polyimide (e.g., Kapton®). In another exemplaryembodiment, the primary growth constraint system 151 comprises acomposite such as E Glass Std Fabric/Epoxy, 0 deg, E Glass UD/Epoxy, 0deg, Kevlar Std Fabric/Epoxy, 0 deg, Kevlar UD/Epoxy, 0 deg, Carbon StdFabric/Epoxy, 0 deg, Carbon UD/Epoxy, 0 deg, Toyobo Zylon® HMFiber/Epoxy. In another exemplary embodiment, the primary growthconstraint system 151 comprises fibers such as Kevlar 49 Aramid Fiber, SGlass Fibers, Carbon Fibers, Vectran UM LCP Fibers, Dyneema, Zylon.

Thickness (t₁) of the primary growth constraint system 151 will dependupon a range of factors including, for example, the material(s) ofconstruction of the primary growth constraint system 151, the overalldimensions of the electrode assembly 106, and the composition of abattery anode and cathode. In some embodiments, for example, the primarygrowth constraint system 151 will comprise a sheet having a thickness inthe range of about 10 to about 100 micrometers. For example, in one suchembodiment, the primary growth constraint system 151 comprises astainless steel sheet (e.g., SS316) having a thickness of about 30 μm.By way of further example, in another such embodiment, the primarygrowth constraint system 151 comprises an aluminum sheet (e.g., 7075-T6)having a thickness of about 40 μm. By way of further example, in anothersuch embodiment, the primary growth constraint system 151 comprises azirconia sheet (e.g., Coorstek YZTP) having a thickness of about 30 μm.By way of further example, in another such embodiment, the primarygrowth constraint system 151 comprises an E Glass UD/Epoxy 0 deg sheethaving a thickness of about 75 μm. By way of further example, in anothersuch embodiment, the primary growth constraint system 151 comprises 12μm carbon fibers at >50% packing density.

Without being bound to any particular theory, methods for gluing, asdescribed herein, may include gluing, soldering, bonding, sintering,press contacting, brazing, thermal spraying joining, clamping, orcombinations thereof. Gluing may include joining the materials withconductive materials such as conducting epoxies, conducting elastomers,mixtures of insulating organic glue filled with conducting metals, suchas nickel filled epoxy, carbon filled epoxy etc. Conductive pastes maybe used to join the materials together and the joining strength could betailored by temperature (sintering), light (UV curing, cross-linking),chemical curing (catalyst based cross linking). Bonding processes mayinclude wire bonding, ribbon bonding, ultrasonic bonding. Weldingprocesses may include ultrasonic welding, resistance welding, laser beamwelding, electron beam welding, induction welding, and cold welding.Joining of these materials can also be performed by using a coatingprocess such as a thermal spray coating such as plasma spraying, flamespraying, arc spraying, to join materials together. For example, anickel or copper mesh can be joined onto a nickel bus using a thermalspray of nickel as a glue.

Members of the anode 110 and cathode structure 112 populations caninclude an electroactive material capable of absorbing and releasing acarrier ion such as lithium, sodium, potassium, calcium, magnesium oraluminum ions. In some embodiments, members of the anode structure 110population include an anodically active electroactive material(sometimes referred to as a negative electrode) and members of thecathode structure 112 population include a cathodically activeelectroactive material (sometimes referred to as a positive electrode).In each of the embodiments and examples recited in this paragraph,negative electrode active material may be a particulate agglomerateelectrode or a monolithic electrode.

Exemplary anodically active electroactive materials include carbonmaterials such as graphite and soft or hard carbons, or any of a rangeof metals, semi-metals, alloys, oxides and compounds capable of formingan alloy with lithium. Specific examples of the metals or semi-metalscapable of constituting the anode material include tin, lead, magnesium,aluminum, boron, gallium, silicon, indium, zirconium, germanium,bismuth, cadmium, antimony, silver, zinc, arsenic, hafnium, yttrium, andpalladium. In one exemplary embodiment, the anodically active materialcomprises aluminum, tin, or silicon, or an oxide thereof, a nitridethereof, a fluoride thereof, or other alloy thereof. In anotherexemplary embodiment, the anodically active material comprises siliconor an alloy thereof.

Exemplary cathode active materials include any of a wide range ofcathode active materials. For example, for a lithium-ion battery, thecathode active material may comprise a cathode material selected fromtransition metal oxides, transition metal sulfides, transition metalnitrides, lithium-transition metal oxides, lithium-transition metalsulfides, and lithium-transition metal nitrides may be selectively used.The transition metal elements of these transition metal oxides,transition metal sulfides, and transition metal nitrides can includemetal elements having a d-shell or f-shell. Specific examples of suchmetal element are Sc, Y, lanthanoids, actinoids, Ti, Zr, Hf, V, Nb, Ta,Cr, Mo, W, Mn, Tc, Re, Fe, Ru, Os, Co, Rh, Ir, Ni, Pb, Pt, Cu, Ag, andAu. Additional cathode active materials include LiCoO₂,LiNi_(0.5)Mn_(1.5)O₄, Li(Ni_(x)Co_(y)Al₂)O₂, LiFePO₄, Li₂MnO₄, V₂O₅,molybdenum oxysulfides, phosphates, silicates, vanadates andcombinations thereof.

In one embodiment, the anode active material is microstructured toprovide a significant void volume fraction to accommodate volumeexpansion and contraction as lithium ions (or other carrier ions) areincorporated into or leave the negative electrode active material duringcharging and discharging processes. In general, the void volume fractionof the anode active material is at least 0.1. Typically, however, thevoid volume fraction of the negative electrode active material is notgreater than 0.8. For example, in one embodiment, the void volumefraction of the negative electrode active material is about 0.15 toabout 0.75. By way of the further example, in one embodiment, the voidvolume fraction of the anode active material is about 0.2 to about 0.7.By way of the further example, in one embodiment, the void volumefraction of the anode active material is about 0.25 to about 0.6.

Depending upon the composition of the microstructured anode activematerial and the method of its formation, the microstructured anodeactive material may comprise macroporous, microporous, or mesoporousmaterial layers or a combination thereof, such as a combination ofmicroporous and mesoporous, or a combination of mesoporous andmacroporous. Microporous material is typically characterized by a poredimension of less than 10 nm, a wall dimension of less than 10 nm, apore depth of 1-50 micrometers, and a pore morphology that is generallycharacterized by a “spongy” and irregular appearance, walls that are notsmooth, and branched pores. Mesoporous material is typicallycharacterized by a pore dimension of 10-50 nm, a wall dimension of 10-50nm, a pore depth of 1-100 micrometers, and a pore morphology that isgenerally characterized by branched pores that are somewhat well definedor dendritic pores. Macroporous material is typically characterized by apore dimension of greater than 50 nm, a wall dimension of greater than50 nm, a pore depth of 1-500 micrometers, and a pore morphology that maybe varied, straight, branched, or dendritic, and smooth or rough-walled.Additionally, the void volume may comprise open or closed voids, or acombination thereof. In one embodiment, the void volume comprises openvoids, that is, the anode active material contains voids having openingsat the lateral surface of the anode active material through whichlithium ions (or other carrier ions) can enter or leave the anode activematerial; for example, lithium ions may enter the anode active materialthrough the void openings after leaving the cathode active material. Inanother embodiment, the void volume comprises closed voids, that is, theanode active material contains voids that are enclosed by anode activematerial. In general, open voids can provide greater interfacial surfacearea for the carrier ions whereas closed voids tend to be lesssusceptible to solid electrolyte interface while each provides room forexpansion of the negative electrode active material upon the entry ofcarrier ions. In certain embodiments, therefore, it is preferred thatthe anode active material comprise a combination of open and closedvoids.

In one embodiment, anode active material comprises porous aluminum, tinor silicon or an alloy thereof. Porous silicon layers may be formed, forexample, by anodization, by etching (e.g., by depositing precious metalssuch as gold, platinum, silver or gold/palladium on the surface ofsingle crystal silicon and etching the surface with a mixture ofhydrofluoric acid and hydrogen peroxide), or by other methods known inthe art such as patterned chemical etching. Additionally, the porousanode active material will generally have a porosity fraction of atleast about 0.1, but less than 0.8 and have a thickness of about 1 toabout 100 micrometers. For example, in one embodiment, anode activematerial comprises porous silicon, has a thickness of about 5 to about100 micrometers, and has a porosity fraction of about 0.15 to about0.75. By way of further example, in one embodiment, anode activematerial comprises porous silicon, has a thickness of about 10 to about80 micrometers, and has a porosity fraction of about 0.15 to about 0.7.By way of further example, in one such embodiment, anode active materialcomprises porous silicon, has a thickness of about 20 to about 50micrometers, and has a porosity fraction of about 0.25 to about 0.6. Byway of further example, in one embodiment, anode active materialcomprises a porous silicon alloy (such as nickel silicide), has athickness of about 5 to about 100 micrometers, and has a porosityfraction of about 0.15 to about 0.75.

In another embodiment, anode active material comprises fibers ofaluminum, tin or silicon, or an alloy thereof. Individual fibers mayhave a diameter (thickness dimension) of about 5 nm to about 10,000 nmand a length generally corresponding to the thickness of the anodeactive material. Fibers (nanowires) of silicon may be formed, forexample, by chemical vapor deposition or other techniques known in theart such as vapor liquid solid (VLS) growth and solid liquid solid (SLS)growth. Additionally, the anode active material will generally have aporosity fraction of at least about 0.1, but less than 0.8 and have athickness of about 1 to about 200 micrometers. For example, in oneembodiment, anode active material comprises silicon nanowires, has athickness of about 5 to about 100 micrometers, and has a porosityfraction of about 0.15 to about 0.75. By way of further example, in oneembodiment, anode active material comprises silicon nanowires, has athickness of about 10 to about 80 micrometers, and has a porosityfraction of about 0.15 to about 0.7. By way of further example, in onesuch embodiment, anode active material comprises silicon nanowires, hasa thickness of about 20 to about 50 micrometers, and has a porosityfraction of about 0.25 to about 0.6. By way of further example, in oneembodiment, anode active material comprises nanowires of a silicon alloy(such as nickel silicide), has a thickness of about 5 to about 100micrometers, and has a porosity fraction of about 0.15 to about 0.75.

In one embodiment, each member of the anode 110 population has a bottom,a top, and a longitudinal axis (A_(E)) extending from the bottom to thetop thereof and in a direction generally perpendicular to the directionin which the alternating sequence of anode structures 110 and cathodestructures 112 progresses. Additionally, each member of the anode 110population has a length (L_(A)) measured along the longitudinal axis(A_(E)) of the anode, a width (W_(A)) measured in the direction in whichthe alternating sequence of anode structures and cathode structuresprogresses, and a height (H_(A)) measured in a direction that isperpendicular to each of the directions of measurement of the length(L_(A)) and the width (W_(A)). Each member of the anode population alsohas a perimeter (P_(A)) that corresponds to the sum of the length(s) ofthe side(s) of a projection of the electrode in a plane that is normalto its longitudinal axis. Exemplary values for the length L_(A), widthW_(A) and height H_(A) are discussed in greater detail above

According to one embodiment, the members of the anode population includeone or more first anode members having a first height, and one or moresecond anode members having a second height that is other than thefirst. For example, in one embodiment, the one or more first anodemembers may have a height selected to allow the anode members to contacta portion of the secondary constraint system in the vertical direction(Z axis). For example, the height of the one or more first anode membersmay be sufficient such that the first anode members extend between andcontact both the first and second secondary growth constraints 158, 160along the vertical axis, such as when at least one of the first anodemembers or a substructure thereof serves as a secondary connectingmember 166. Furthermore, according to one embodiment, one or more secondanode members may have a height that is less than the one or more firstanode members, such that for example the one or more second anodemembers do not fully extend to contact both of the first and secondsecondary growth constraints 158, 160. In yet another embodiment, thedifferent heights for the one or more first anode members and one ormore second anode members may be selected to accommodate a predeterminedshape for the electrode assembly 106, such as an electrode assemblyshape having a different heights along one or more of the longitudinaland/or transverse axis, and/or to provide predetermined performancecharacteristics for the secondary battery.

The perimeter (P_(A)) of the members of the anode population willsimilarly vary depending upon the energy storage device and its intendeduse. In general, however, members of the anode population will typicallyhave a perimeter (P_(A)) within the range of about 0.025 mm to about 25mm. For example, in one embodiment, the perimeter (P_(A)) of each memberof the anode population will be in the range of about 0.1 mm to about 15mm. By way of further example, in one embodiment, the perimeter (P_(A))of each member of the anode population will be in the range of about 0.5mm to about 10 mm.

In general, members of the anode population have a length (L_(A)) thatis substantially greater than each of its width (W_(A)) and its height(H_(A)). For example, in one embodiment, the ratio of L_(A) to each ofW_(A) and HA is at least 5:1, respectively (that is, the ratio of L_(A)to W_(A) is at least 5:1, respectively and the ratio of L_(A) to H_(A)is at least 5:1, respectively), for each member of the anode population.By way of further example, in one embodiment the ratio of L_(A) to eachof W_(A) and H_(A) is at least 10:1. By way of further example, in oneembodiment, the ratio of L_(A) to each of W_(A) and H_(A) is at least15:1. By way of further example, in one embodiment, the ratio of L_(A)to each of W_(A) and H_(A) is at least 20:1, for each member of theanode population.

Additionally, it is generally preferred that members of the anodepopulation have a length (L_(A)) that is substantially greater than itsperimeter (P_(A)); for example, in one embodiment, the ratio of L_(A) toPA is at least 1.25:1, respectively, for each member of the anodepopulation. By way of further example, in one embodiment the ratio ofL_(A) to P_(A) is at least 2.5:1, respectively, for each member of theanode population. By way of further example, in one embodiment, theratio of L_(A) to P_(A) is at least 3.75:1, respectively, for eachmember of the anode population.

In one embodiment, the ratio of the height (H_(A)) to the width (WA) ofthe members of the anode population is at least 0.4:1, respectively. Forexample, in one embodiment, the ratio of H_(A) to W_(A) will be at least2:1, respectively, for each member of the anode population. By way offurther example, in one embodiment the ratio of H_(A) to W_(A) will beat least 10:1, respectively. By way of further example, in oneembodiment the ratio of H_(A) to W_(A) will be at least 20:1,respectively. Typically, however, the ratio of H_(A) to W_(A) willgenerally be less than 1,000:1, respectively. For example, in oneembodiment the ratio of H_(A) to W_(A) will be less than 500:1,respectively. By way of further example, in one embodiment the ratio ofH_(A) to W_(A) will be less than 100:1, respectively. By way of furtherexample, in one embodiment the ratio of H_(A) to W_(A) will be less than10:1, respectively. By way of further example, in one embodiment theratio of H_(A) to W_(A) will be in the range of about 2:1 to about100:1, respectively, for each member of the anode population.

Each member of the cathode population has a bottom, a top, and alongitudinal axis (A_(CE)) extending from the bottom to the top thereofand in a direction generally perpendicular to the direction in which thealternating sequence of anode structures and cathode structuresprogresses. Additionally, each member of the cathode population has alength (L_(C)) measured along the longitudinal axis (A_(CE)), a width(W_(C)) measured in the direction in which the alternating sequence ofanode structures and cathode structures progresses, and a height (H_(C))measured in a direction that is perpendicular to each of the directionsof measurement of the length (L_(C)) and the width (W_(C)). Each memberof the cathode population also has a perimeter (P_(C)) that correspondsto the sum of the length(s) of the side(s) of a projection of thecathode in a plane that is normal to its longitudinal axis.

According to one embodiment, the members of the cathode populationinclude one or more first cathode members having a first height, and oneor more second cathode members having a second height that is other thanthe first. For example, in one embodiment, the one or more first cathodemembers may have a height selected to allow the cathode members tocontact a portion of the secondary constraint system in the verticaldirection (Z axis). For example, the height of the one or more firstcathode members may be sufficient such that the first cathode membersextend between and contact both the first and second secondary growthconstraints 158, 160 along the vertical axis, such as when at least oneof the first cathode members or a substructure thereof serves as asecondary connecting member 166. Furthermore, according to oneembodiment, one or more second cathode members may have a height that isless than the one or more first cathode members, such that for examplethe one or more second cathode members do not fully extend to contactboth of the first and second secondary growth constraints 158, 160. Inyet another embodiment, the different heights for the one or more firstcathode members and one or more second cathode members may be selectedto accommodate a predetermined shape for the electrode assembly 106,such as an electrode assembly shape having a different heights along oneor more of the longitudinal and/or transverse axis, and/or to providepredetermined performance characteristics for the secondary battery.

The perimeter (P_(C)) of the members of the cathode population will alsovary depending upon the energy storage device and its intended use. Ingeneral, however, members of the cathode population will typically havea perimeter (P_(C)) within the range of about 0.025 mm to about 25 mm.For example, in one embodiment, the perimeter (P_(C)) of each member ofthe cathode population will be in the range of about 0.1 mm to about 15mm. By way of further example, in one embodiment, the perimeter (P_(C))of each member of the cathode population will be in the range of about0.5 mm to about 10 mm.

In general, each member of the cathode population has a length (L_(C))that is substantially greater than width (W_(C)) and substantiallygreater than its height (H_(C)). For example, in one embodiment, theratio of L_(C) to each of W_(C) and H_(C) is at least 5:1, respectively(that is, the ratio of L_(C) to W_(C) is at least 5:1, respectively andthe ratio of L_(C) to H_(C) is at least 5:1, respectively), for eachmember of the cathode population. By way of further example, in oneembodiment the ratio of L_(C) to each of W_(C) and H_(C) is at least10:1 for each member of the cathode population. By way of furtherexample, in one embodiment, the ratio of L_(C) to each of W_(C) andH_(C) is at least 15:1 for each member of the cathode population. By wayof further example, in one embodiment, the ratio of L_(C) to each ofW_(C) and H_(C) is at least 20:1 for each member of the cathodepopulation.

Additionally, it is generally preferred that members of the cathodepopulation have a length (L_(C)) that is substantially greater than itsperimeter (P_(C)); for example, in one embodiment, the ratio of L_(C) toP_(C) is at least 1.25:1, respectively, for each member of the cathodepopulation. By way of further example, in one embodiment the ratio ofL_(C) to P_(C) is at least 2.5:1, respectively, for each member of thecathode population. By way of further example, in one embodiment, theratio of L_(C) to P_(C) is at least 3.75:1, respectively, for eachmember of the cathode population.

In one embodiment, the ratio of the height (H_(C)) to the width (W_(C))of the members of the cathode population is at least 0.4:1,respectively. For example, in one embodiment, the ratio of H_(C) toW_(E) will be at least 2:1, respectively, for each member of the cathodepopulation. By way of further example, in one embodiment the ratio ofH_(C) to W_(C) will be at least 10:1, respectively, for each member ofthe cathode population. By way of further example, in one embodiment theratio of H_(C) to W_(C) will be at least 20:1, respectively, for eachmember of the cathode population. Typically, however, the ratio of H_(C)to W_(C) will generally be less than 1,000:1, respectively, for eachmember of the cathode population. For example, in one embodiment theratio of H_(C) to W_(C) will be less than 500:1, respectively, for eachmember of the cathode population. By way of further example, in oneembodiment the ratio of H_(C) to W_(C) will be less than 100:1,respectively. By way of further example, in one embodiment the ratio ofH_(C) to W_(C) will be less than 10:1, respectively. By way of furtherexample, in one embodiment the ratio of H_(C) to W_(C) will be in therange of about 2:1 to about 100:1, respectively, for each member of thecathode population.

In one embodiment the anode current conductor layer 136 comprised byeach member of the anode population has a length L_(NC) that is at least50% of the length L_(NE) of the member comprising such anode currentcollector. By way of further example, in one embodiment the anodecurrent conductor layer 136 comprised by each member of the anodepopulation has a length L_(NC) that is at least 60% of the length L_(NE)of the member comprising such anode current collector. By way of furtherexample, in one embodiment the anode current conductor layer 136comprised by each member of the anode population has a length L_(NC)that is at least 70% of the length L_(NE) of the member comprising suchanode current collector. By way of further example, in one embodimentthe anode current conductor layer 136 comprised by each member of theanode population has a length L_(NC) that is at least 80% of the lengthL_(NE) of the member comprising such anode current collector. By way offurther example, in one embodiment the anode current conductor 136comprised by each member of the anode population has a length L_(NC)that is at least 90% of the length L_(NE) of the member comprising suchanode current collector.

In one embodiment, the cathode current conductor 140 comprised by eachmember of the cathode population has a length L_(PC) that is at least50% of the length L_(PE) of the member comprising such cathode currentcollector. By way of further example, in one embodiment the cathodecurrent conductor 140 comprised by each member of the cathode populationhas a length L_(PC) that is at least 60% of the length L_(PE) of themember comprising such cathode current collector. By way of furtherexample, in one embodiment the cathode current conductor 140 comprisedby each member of the cathode population has a length L_(PC) that is atleast 70% of the length L_(PE) of the member comprising such cathodecurrent collector. By way of further example, in one embodiment thecathode current conductor 140 comprised by each member of the cathodepopulation has a length L_(PC) that is at least 80% of the length L_(PE)of the member comprising such cathode current collector. By way offurther example, in one embodiment the cathode current conductor 140comprised by each member of the cathode population has a length L_(PC)that is at least 90% of the length L_(PE) of the member comprising suchcathode current collector.

In one embodiment, being positioned between the anode active materiallayer and the separator, anode current collector 136 may facilitate moreuniform carrier ion transport by distributing current from the anodecurrent collector across the surface of the anode active material layer.This, in turn, may facilitate more uniform insertion and extraction ofcarrier ions and thereby reduce stress in the anode active materialduring cycling; since anode current collector 136 distributes current tothe surface of the anode active material layer facing the separator, thereactivity of the anode active material layer for carrier ions will bethe greatest where the carrier ion concentration is the greatest. In yetanother embodiment, the positions of the anode current collector 136 andthe anode active material layer may be reversed.

According to one embodiment, each member of the cathode structurepopulation has a cathode current collector 140 that may be disposed, forexample, between the cathode backbone and the cathode active materiallayer. Furthermore, one or more of the anode current collector 136 andcathode electrode current collector 140 may comprise a metal such asaluminum, carbon, chromium, gold, nickel, NiP, palladium, platinum,rhodium, ruthenium, an alloy of silicon and nickel, titanium, or acombination thereof (see “Current collectors for positive electrodes oflithium-based batteries” by A. H. Whitehead and M. Schreiber, Journal ofthe Electrochemical Society, 152(11) A2105-A2113 (2005)). By way offurther example, in one embodiment, cathode current collector 140comprises gold or an alloy thereof such as gold silicide. By way offurther example, in one embodiment, cathode current collector 140comprises nickel or an alloy thereof such as nickel silicide.

In an alternative embodiment, the positions of the cathode currentcollector layer and the cathode electrode active material layer may bereversed, for example such that that the cathode electrode currentcollector layer is positioned between the separator layer and thecathode active material layer. In such embodiments, the cathodeelectrode current collector 140 for the immediately adjacent cathodeactive material layer comprises an ionically permeable conductor havinga composition and construction as described in connection with the anodecurrent collector layer; that is, the cathode current collector layercomprises a layer of an ionically permeable conductor material that isboth ionically and electrically conductive. In this embodiment, thecathode electrode current collector layer has a thickness, an electricalconductivity, and an ionic conductivity for carrier ions thatfacilitates the movement of carrier ions between an immediately adjacentcathode electrode active material layer on one side of the cathodeelectrode current collector layer and an immediately adjacent separatorlayer on the other side of the cathode electrode current collector layerin an electrochemical stack.

Electrically insulating separator layers 130 may surround andelectrically isolate each member of the anode structure 110 populationfrom each member of the cathode structure 112 population. Electricallyinsulating separator layers 130 will typically include a microporousseparator material that can be permeated with a non-aqueous electrolyte;for example, in one embodiment, the microporous separator materialincludes pores having a diameter of at least 50 Å, more typically in therange of about 2,500 Å, and a porosity in the range of about 25% toabout 75%, more typically in the range of about 35-55%. Additionally,the microporous separator material may be permeated with a non-aqueouselectrolyte to permit conduction of carrier ions between adjacentmembers of the anode and cathode populations. In certain embodiments,for example, and ignoring the porosity of the microporous separatormaterial, at least 70 vol % of electrically insulating separatormaterial between a member of the anode structure 110 population and thenearest member(s) of the cathode structure 112 population (i.e., an“adjacent pair”) for ion exchange during a charging or discharging cycleis a microporous separator material; stated differently, microporousseparator material constitutes at least 70 vol % of the electricallyinsulating material between a member of the anode structure 110population and the nearest member of the cathode 112 structurepopulation. By way of further example, in one embodiment, and ignoringthe porosity of the microporous separator material, microporousseparator material constitutes at least 75 vol % of the electricallyinsulating separator material layer between adjacent pairs of members ofthe anode structure 110 population and members of the cathode structure112 population, respectively. By way of further example, in oneembodiment, and ignoring the porosity of the microporous separatormaterial, the microporous separator material constitutes at least 80 vol% of the electrically insulating separator material layer betweenadjacent pairs of members of the anode structure 110 population andmembers of the cathode structure 112 population, respectively. By way offurther example, in one embodiment, and ignoring the porosity of themicroporous separator material, the microporous separator materialconstitutes at least 85 vol % of the electrically insulating separatormaterial layer between adjacent pairs of members of the anode structure110 population and members of the cathode structure 112 population,respectively. By way of further example, in one embodiment, and ignoringthe porosity of the microporous separator material, the microporousseparator material constitutes at least 90 vol % of the electricallyinsulating separator material layer between adjacent pairs of members ofthe anode structure 110 population and member of the cathode structure112 population, respectively. By way of further example, in oneembodiment, and ignoring the porosity of the microporous separatormaterial, the microporous separator material constitutes at least 95 vol% of the electrically insulating separator material layer betweenadjacent pairs of members of the anode structure 110 population andmembers of the cathode structure 112 population, respectively. By way offurther example, in one embodiment, and ignoring the porosity of themicroporous separator material, the microporous separator materialconstitutes at least 99 vol % of the electrically insulating separatormaterial layer between adjacent pairs of members of the anode structure110 population and members of the cathode structure 112 population,respectively.

In one embodiment, the microporous separator material comprises aparticulate material and a binder, and has a porosity (void fraction) ofat least about 20 vol. % The pores of the microporous separator materialwill have a diameter of at least 50 Å and will typically fall within therange of about 250 to 2,500 Å. The microporous separator material willtypically have a porosity of less than about 75%. In one embodiment, themicroporous separator material has a porosity (void fraction) of atleast about 25 vol %. In one embodiment, the microporous separatormaterial will have a porosity of about 35-55%.

The binder for the microporous separator material may be selected from awide range of inorganic or polymeric materials. For example, in oneembodiment, the binder is an organic material selected from the groupconsisting of silicates, phosphates, aluminates, aluminosilicates, andhydroxides such as magnesium hydroxide, calcium hydroxide, etc. Forexample, in one embodiment, the binder is a fluoropolymer derived frommonomers containing vinylidene fluoride, hexafluoropropylene,tetrafluoropropene, and the like. In another embodiment, the binder is apolyolefin such as polyethylene, polypropylene, or polybutene, havingany of a range of varying molecular weights and densities. In anotherembodiment, the binder is selected from the group consisting ofethylene-diene-propene terpolymer, polystyrene, polymethyl methacrylate,polyethylene glycol, polyvinyl acetate, polyvinyl butyral, polyacetal,and polyethyleneglycol diacrylate. In another embodiment, the binder isselected from the group consisting of methyl cellulose, carboxymethylcellulose, styrene rubber, butadiene rubber, styrene-butadiene rubber,isoprene rubber, polyacrylamide, polyvinyl ether, polyacrylic acid,polymethacrylic acid, and polyethylene oxide. In another embodiment, thebinder is selected from the group consisting of acrylates, styrenes,epoxies, and silicones. In another embodiment, the binder is a copolymeror blend of two or more of the aforementioned polymers.

The particulate material comprised by the microporous separator materialmay also be selected from a wide range of materials. In general, suchmaterials have a relatively low electronic and ionic conductivity atoperating temperatures and do not corrode under the operating voltagesof the battery electrode or current collector contacting the microporousseparator material. For example, in one embodiment, the particulatematerial has a conductivity for carrier ions (e.g., lithium) of lessthan 1×10⁻⁴ S/cm. By way of further example, in one embodiment, theparticulate material has a conductivity for carrier ions of less than1×10⁻⁵ S/cm. By way of further example, in one embodiment, theparticulate material has a conductivity for carrier ions of less than1×10⁻⁶ S/cm. Exemplary particulate materials include particulatepolyethylene, polypropylene, a TiO₂-polymer composite, silica aerogel,fumed silica, silica gel, silica hydrogel, silica xerogel, silica sol,colloidal silica, alumina, titania, magnesia, kaolin, talc, diatomaceousearth, calcium silicate, aluminum silicate, calcium carbonate, magnesiumcarbonate, or a combination thereof. For example, in one embodiment, theparticulate material comprises a particulate oxide or nitride such asTiO₂, SiO₂, Al₂O₃,GeO₂, B₂O₃, Bi₂O₃, BaO, ZnO, ZrO₂, BN, Si₃N₄, Ge₃N₄.See, for example, P. Arora and J. Zhang, “Battery Separators” ChemicalReviews 2004, 104, 4419-4462). In one embodiment, the particulatematerial will have an average particle size of about 20 nm to 2micrometers, more typically 200 nm to 1.5 micrometers. In oneembodiment, the particulate material will have an average particle sizeof about 500 nm to 1 micrometer.

In an alternative embodiment, the particulate material comprised by themicroporous separator material may be bound by techniques such assintering, binding, curing, etc. while maintaining the void fractiondesired for electrolyte ingress to provide the ionic conductivity forthe functioning of the battery.

Microporous separator materials may be deposited, for example, byelectrophoretic deposition of a particulate separator material in whichparticles are coalesced by surface energy such as electrostaticattraction or van der Waals forces, slurry deposition (including spin orspray coating) of a particulate separator material, screen printing, dipcoating, and electrostatic spray deposition. Binders may be included inthe deposition process; for example, the particulate material may beslurry deposited with a dissolved binder that precipitates upon solventevaporation, electrophoretically deposited in the presence of adissolved binder material, or co-electrophoretically deposited with abinder and insulating particles etc. Alternatively, or additionally,binders may be added after the particles are deposited into or onto theelectrode structure; for example, the particulate material may bedispersed in an organic binder solution and dip coated or spray-coated,followed by drying, melting, or cross-linking the binder material toprovide adhesion strength.

In an assembled energy storage device, the microporous separatormaterial is permeated with a non-aqueous electrolyte suitable for use asa secondary battery electrolyte. Typically, the non-aqueous electrolytecomprises a lithium salt dissolved in an organic solvent. Exemplarylithium salts include inorganic lithium salts such as LiClO₄, LiBF₄,LiPF₆, LiAsF₆, LiCl, and LiBr; and organic lithium salts such asLiB(C₆H₅)₄, LiN(SO₂CF₃)₂, LiN(SO₂CF₃)₃, LiNSO₂CF₃, LiNSO₂CF₅,LiNSO₂C₄F₉, LiNSO₂C₅F₁₁, LiNSO₂C₆F₁₃, and LiNSO₂C₇F₁₅. Exemplary organicsolvents to dissolve the lithium salt include cyclic esters, chainesters, cyclic ethers, and chain ethers. Specific examples of the cyclicesters include propylene carbonate, butylene carbonate, γ-butyrolactone,vinylene carbonate, 2-methyl-γ-butyrolactone, acetyl-γ-butyrolactone,and γ-valerolactone. Specific examples of the chain esters includedimethyl carbonate, diethyl carbonate, dibutyl carbonate, dipropylcarbonate, methyl ethyl carbonate, methyl butyl carbonate, methyl propylcarbonate, ethyl butyl carbonate, ethyl propyl carbonate, butyl propylcarbonate, alkyl propionates, dialkyl malonates, and alkyl acetates.Specific examples of the cyclic ethers include tetrahydrofuran,alkyltetrahydrofurans, dialkyltetrahydrofurans, alkoxytetrahydrofurans,dialkoxytetrahydrofurans, 1,3-dioxolane, alkyl-1,3-dioxolanes, and1,4-dioxolane. Specific examples of the chain ethers include1,2-dimethoxyethane, 1,2-diethoxythane, diethyl ether, ethylene glycoldialkyl ethers, diethylene glycol dialkyl ethers, triethylene glycoldialkyl ethers, and tetraethylene glycol dialkyl ethers.

Furthermore, according to one embodiment, components of the secondarybattery 102 including the microporous separator 130 and other anode 110and/or cathode 112 structures comprise a configuration and compositionthat allow the components to function, even in a case where expansion ofanode active material 132 occurs during charge and discharge of thesecondary battery 102. That is, the components may be structured suchthat failure of the components due to expansion of the electrode activematerial 132 during charge/discharge thereof is within acceptablelimits.

INCORPORATION BY REFERENCE

All publications and patents mentioned herein, including those itemslisted below, are hereby incorporated by reference in their entirety forall purposes as if each individual publication or patent wasspecifically and individually incorporated by reference. In case ofconflict, the present application, including any definitions herein,will control.

Equivalents

While specific embodiments have been discussed, the above specificationis illustrative, and not restrictive. Many variations will becomeapparent to those skilled in the art upon review of this specification.The full scope of the embodiments should be determined by reference tothe claims, along with their full scope of equivalents, and thespecification, along with such variations.

Unless otherwise indicated, all numbers expressing quantities ofingredients, reaction conditions, and so forth used in the specificationand claims are to be understood as being modified in all instances bythe term “about.” Accordingly, unless indicated to the contrary, thenumerical parameters set forth in this specification and attached claimsare approximations that may vary depending upon the desired propertiessought to be obtained.

What is claimed is:
 1. A secondary battery for cycling between a chargedand a discharged state, the secondary battery comprising a batteryenclosure, an electrode assembly, carrier ions, and a non-aqueous liquidelectrolyte within the battery enclosure, wherein the electrode assemblycomprises a population of anode structures, a population of cathodestructures, and an electrically insulating microporous separatormaterial electrically separating members of the anode and cathodestructure populations, wherein the anode and cathode structurepopulations are arranged in an alternating sequence in a longitudinaldirection, each member of the anode structure population has a firstcross-sectional area, A₁ when the secondary battery is in the chargedstate and a second cross-sectional area, A₂, when the secondary batteryis in the discharged state, each member of the cathode structurepopulation has a first cross-sectional area, C₁ when the secondarybattery is in the charged state and a second cross-sectional area, C₂,when the secondary battery is in the discharged state, and thecross-sectional areas of the members of the anode and cathode structurepopulations are measured in a first longitudinal plane that is parallelto the longitudinal direction; the electrode assembly further comprisesa set of electrode constraints that at least partially restrains growthof the electrode assembly in the longitudinal direction upon cycling ofthe secondary battery between the charged and discharged states; eachmember of the population of cathode structures comprises a layer of acathode active material comprising filler particles that arecompressible and elastic, and each member of the population of anodestructures comprises a layer of an anode active material having acapacity to accept more than one mole of carrier ion per mole of anodeactive material when the secondary battery is charged from a dischargedstate to a charged state, A₁ is greater than A₂ for each of the membersof a subset of the anode structure population and C₁ is less than C₂ foreach of the members of a subset of the cathode structure population, andwherein a difference C₂−C₁ does not exceed a difference A₁−A₂ duringcycling of the secondary battery; wherein a ratio of C₂ to C₁ for eachof the members of the subset of the cathode structure population is atleast 1.1:1; and the charged state is at least 75% of the rated capacityof the secondary battery, and the discharged state is less than 25% ofthe rated capacity of the secondary battery.
 2. The secondary battery ofclaim 1, wherein the anode structure population subset has a firstmedian cross-sectional area MA_(A1) when the secondary battery is in thecharged state and a second median cross-sectional area MA_(A2) when thesecondary battery is in the discharged state, and the cathode structurepopulation subset has a first median cross-sectional area MA_(C1) whenthe secondary battery is in the charged state and a second mediancross-sectional area MA_(C2) when the secondary battery is in thedischarged state, wherein MA_(A1) is greater than MA_(A2) and MA_(C1) isless than MA_(C2).
 3. The secondary battery of claim 1, wherein theanode structure population subset comprises at least 10% of the totalpopulation of anode structures, and the cathode structure populationsubset comprises at least 10% of the total population of cathodestructures.
 4. The secondary battery of claim 1, wherein each member ofthe cathode population comprises orthogonal height H_(C), width W_(C),and length L_(C) directions, and wherein a ratio of the length L_(C) toeach of the height H_(c) and the width W_(C) is at least 5:1.
 5. Thesecondary battery of claim 1, wherein at least one member of the anodestructure population subset has a first median cross-sectional area,ML_(A1) when the secondary battery is in the charged state, and a secondmedian cross-sectional area, ML_(A2) when the secondary battery is inthe discharged state, and at least one member of the cathode structurepopulation subset has a first median cross-sectional area, ML_(C1) whenthe secondary battery is in the charged state, and a second mediancross-sectional area ML_(C2) when the secondary battery is in thedischarged state, where the median cross-sectional areas ML_(A1),ML_(A2), ML_(C1) and ML_(C2) are measured in a plurality of longitudinalplanes parallel to the longitudinal direction for each member, andwherein ML_(A1) is greater than ML_(A2) for each of the members of thesubset of the anode structure population and ML_(C1) is less thanML_(C2) for each of the members of the subset of the cathode structurepopulation.
 6. The secondary battery of claim 1, wherein C₁ is in therange of from 2×10² μm² to 3×10⁷ μm².
 7. The secondary battery of claim1, wherein C₂ is in the range of from 1.0×10³ μm² to 1.0×10⁷ μm².
 8. Thesecondary battery of claim 1, wherein A₁ is in the range of from 100 μm²to 1.5×10⁷ μm².
 9. The secondary battery of claim 1, wherein A₂ is inthe range of from 500 μm² to 3×10⁷ μm².
 10. The secondary battery ofclaim 1, wherein the ratio of C₂ to C₁ is at least 3:1.
 11. Thesecondary battery of claim 1, wherein the ratio of the A₂ to A₁ is atleast 1.01:1.
 12. The secondary battery of claim 1, wherein the ratio ofthe A₂ to A₁ is at least 3:1.
 13. The secondary battery of claim 2,wherein the first median cross-sectional area MA_(A1) of the subset ofthe population of anode structures is in the range of from 100 μm² to1.5×10⁷ μm², and the second median cross sectional area MA_(A2) of thesubset of the population of anode structures is in the range of from 500μm² to 3×10⁷ μm².
 14. The secondary battery of claim 2, wherein thesecond median cross-sectional area MA_(C2) of the subset of thepopulation of cathode structures is in the range of from 1.01×10² μm² to1.5×10¹⁰ μm², and the first median cross-sectional MA_(C1) of the subsetof the population of cathode structures is in the range of from 1×10²μm² to 3×10⁷ μm².
 15. The secondary battery of claim 2, wherein a ratioof the first median cross-sectional area MA_(A1) of the subset of thepopulation of anode structures to the second median cross sectional areaMA_(A2) of the subset of the population of anode structures is at least1.01:1.
 16. The secondary battery of claim 2, wherein a ratio of thefirst median cross-sectional area MA_(A1) of the subset of thepopulation of anode structures to the second median cross sectional areaMA_(A2) of the subset of the population of anode structures is at least3:1.
 17. The secondary battery of claim 2, wherein the ratio of thesecond median cross-sectional area MA_(C2) of the subset of thepopulation of cathode structures to the first median cross-sectionalMA_(C1) of the subset of the population of cathode structures is atleast 3:1.
 18. The secondary battery of claim 5, wherein the firstmedian cross-sectional area ML_(A1) of the subset of the population ofanode structures is in the range of from 100 μm² to 1.5×10⁷ μm², and thesecond median cross sectional area ML_(A2) of the subset of thepopulation of anode structures is in the range of from 500 μm² to 3×10⁷μm².
 19. The secondary battery of claim 5, wherein the second mediancross-sectional area ML_(C2) of the subset of the population of cathodestructures is in the range of from 1.01×10² μm² to 1.5×10¹⁰ μm², and thefirst median cross-sectional ML_(C1) of the subset of the population ofcathode structures is in the range of from 1×10² μm² to 3×10⁷ μm². 20.The secondary battery of claim 5, wherein a ratio of the first mediancross-sectional area ML_(A1) of the subset of the population of anodestructures to the second median cross sectional area ML_(A2) of thesubset of the population of anode structures is at least 1.01:1.
 21. Thesecondary battery of claim 5, wherein a ratio of the first mediancross-sectional area ML_(A1) of the subset of the population of anodestructures to the second median cross sectional area ML_(A2) of thesubset of the population of anode structures is at least 3:1.
 22. Thesecondary battery of claim 5 wherein a ratio of the second mediancross-sectional area ML_(C2) of the subset of the population of cathodestructures to the first median cross-sectional ML_(C1) of the subset ofthe population of cathode structures is at least 1.1:1.
 23. Thesecondary battery of claim 5 wherein a ratio of the second mediancross-sectional area ML_(C2) of the subset of the population of cathodestructures to the first median cross-sectional ML_(C1) of the subset ofthe population of cathode structures is at least 3:1.
 24. The secondarybattery according to claim 1, wherein members of the population ofcathode structures comprise a layer of cathode active material that isporous, and wherein the layer of cathode active material has a firstporosity P₁ when the secondary battery is in a charged state, and asecond porosity P₂ when the secondary battery is in a discharged state,the first porosity P₁ being less than the second porosity P₂.
 25. Thesecondary battery according to claim 24, wherein the first porosity P₁is no more than 30%, and the second porosity P₂ is at least about 50%.26. The secondary battery according to claim 24, wherein a ratio of thesecond porosity P₂ to the first porosity P₁ is at least 1.1:1.
 27. Thesecondary battery according to claim 24, wherein a ratio of the secondporosity P₂ to the first porosity P₁ is at least 2:1.
 28. The secondarybattery according to claim 1, wherein the secondary battery has an arealcapacity of at least 5 mA·h/cm² at 0.1 C.
 29. The secondary battery ofclaim 1, wherein the cathode active material layers of members of thepopulation of cathode structures comprise particles of cathode activematerials dispersed in a matrix.
 30. The secondary battery of claim 29,wherein the cathode active material layers comprises particles ofcathode active material selected from the group consisting of transitionmetal oxides, transition metal sulfides, transition metal nitrides,lithium-transition metal oxides, lithium-transition metal sulfides, andlithium-transition metal nitrides, dispersed in the matrix, the matrixcomprising a polymeric material.
 31. The secondary battery of claim 1wherein the set of electrode constraints comprises: a primary constraintsystem comprising first and second primary growth constraints and atleast one primary connecting member, the first and second primary growthconstraints separated from each other in the longitudinal direction andthe at least one primary connecting member connecting the first andsecond primary growth constraints, wherein the primary constraint systemat least partially restrains growth of the electrode assembly in thelongitudinal direction upon cycling of the secondary battery.
 32. Thesecondary battery of claim 31, wherein the primary constraint systemrestrains growth of the electrode assembly in the longitudinaldirection, such that any increase in the Feret diameter of the electrodeassembly in the longitudinal direction over 20 consecutive cycles of thesecondary battery is less than 20%.
 33. The secondary battery of claim31, wherein the set of electrode constraints further comprises: asecondary constraint system comprising first and second secondary growthconstraints separated in a second direction and connected by at leastone secondary connecting member, wherein the secondary constraint systemat least partially restrains growth of the electrode assembly in asecond direction upon cycling of the secondary battery, the seconddirection being orthogonal to the longitudinal direction.
 34. Thesecondary battery of claim 33, wherein the secondary growth constraintsystem restrains growth of the electrode assembly in the seconddirection such that any increase in the Feret diameter of the electrodeassembly in the second direction over 20 consecutive cycles uponrepeated cycling of the secondary battery is less than 20%.